Probability of A occurringP(A)

Sum of all possible outcomes = 1

the collection of all possible outcomes of a chance experimentRoll a die S=123456

Of Occurrences of Event

Trials

Not rolling a even EC=135

The long run relative frequency will approach the actual probability as the number of trails increasesCoins 2 10 20

any collection of outcomes from the sample space

Rolling a prime E= 235

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

the collection of all possible outcomes of a chance experimentRoll a die S=123456

Of Occurrences of Event

Trials

Not rolling a even EC=135

The long run relative frequency will approach the actual probability as the number of trails increasesCoins 2 10 20

any collection of outcomes from the sample space

Rolling a prime E= 235

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Of Occurrences of Event

Trials

Not rolling a even EC=135

The long run relative frequency will approach the actual probability as the number of trails increasesCoins 2 10 20

any collection of outcomes from the sample space

Rolling a prime E= 235

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

The long run relative frequency will approach the actual probability as the number of trails increasesCoins 2 10 20

any collection of outcomes from the sample space

Rolling a prime E= 235

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

any collection of outcomes from the sample space

Rolling a prime E= 235

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Consists of all outcomes that are not in the event

Not rolling a even EC=135

P(A) = 1 ndash P(A)

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

two events have no outcomes in common

Roll a ldquo2rdquo or a ldquo5rdquoDraw a Black card or a Diamond

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

two events have outcomes in common

Draw a Black card or a Spade

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

the event A or B happeningconsists of all outcomes that are in at least one of the two eventsDraw a Black card or a Diamond

BAE

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Draw a Black card or a DiamondP(B U D) = P(B) + P(D)

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

the event A and B happeningconsists of all outcomes that are in both events

Draw a Black card and a 7

BAE

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

P(B S) = P(B)bullP(S)Draw a Black card and a 7

BAE U

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

the event A or B happening BUT WE CANrsquoT Double CountDraw a Black card or a 7

P(B or 7) = P(B) + P(7) ndash P(B and 7)

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Used to display relationships between events

Helpful in calculating probabilities

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Com Sci

Statistics amp Computer Science amp not Calculus

Stat Cal

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Com Sci

Stat Cal

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

(a) P ( has pierced ears )

(b) P( is a male or has pierced ears )

(c)P( is a female or has pierced ears )

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Rule 1 Legitimate ValuesFor any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Rule 3 Complement

For any event E

P(E) + P(not E) = 1Or

P(not E) = 1 ndash P(E)

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Rule 4 Addition (A or B)If two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Ex 1) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

Two events are independent if knowing that one will occur (or has occurred) does not change the probability that the other occursFlip a Coin and Get Heads Flip a coin again

P(T)

Draw a 7 from a deck Draw another card P(8)

Independent

Not independent

Rule 5 Multiplication

If two events A amp B are independent

General rule

P(B) P(A) B) ampP(A

A)|P(B P(A) B) ampP(A

The probability that a student will receive a state grant is 13 while the probability she will be awarded a federal grant is frac12

If whether or not she receives one grant is not influenced by whether or not she receives the other what is the probability of her receiving both grants

Suppose a reputed psychic in an extrasensory perception (ESP) experiment has called heads or tails correctly on TEN successive coin flips What is the probability that her guessing would have yielded this perfect score

Tree Diagrams

Consider flipping a coin twice

What is the probability of getting two heads

Sample Space

HH HT TH TT

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Rule 5 Multiplication

If two events A amp B are independent

General rule

P(B) P(A) B) ampP(A

A)|P(B P(A) B) ampP(A

The probability that a student will receive a state grant is 13 while the probability she will be awarded a federal grant is frac12

If whether or not she receives one grant is not influenced by whether or not she receives the other what is the probability of her receiving both grants

Suppose a reputed psychic in an extrasensory perception (ESP) experiment has called heads or tails correctly on TEN successive coin flips What is the probability that her guessing would have yielded this perfect score

Tree Diagrams

Consider flipping a coin twice

What is the probability of getting two heads

Sample Space

HH HT TH TT

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

The probability that a student will receive a state grant is 13 while the probability she will be awarded a federal grant is frac12

If whether or not she receives one grant is not influenced by whether or not she receives the other what is the probability of her receiving both grants

Suppose a reputed psychic in an extrasensory perception (ESP) experiment has called heads or tails correctly on TEN successive coin flips What is the probability that her guessing would have yielded this perfect score

Tree Diagrams

Consider flipping a coin twice

What is the probability of getting two heads

Sample Space

HH HT TH TT

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Suppose a reputed psychic in an extrasensory perception (ESP) experiment has called heads or tails correctly on TEN successive coin flips What is the probability that her guessing would have yielded this perfect score

Tree Diagrams

Consider flipping a coin twice

What is the probability of getting two heads

Sample Space

HH HT TH TT

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Tree Diagrams

Consider flipping a coin twice

What is the probability of getting two heads

Sample Space

HH HT TH TT

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Getting Tails Twice

Tree Diagrams

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Example Teens with Online ProfilesThe Pew Internet and American Life Project finds that 93 of teenagers (ages

12 to 17) use the Internet and that 55 of online teens have posted a profile on a social-networking site

What percent of teens are online and have posted a profile

5115 of teens are online and have posted a profile

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 3) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that both cookies are stale

Can you assume they are independent

00250505D) amp P(D

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 5) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 6) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that exactly one cookie is stale

P(exactly one) = P(S amp SC) or P(SC amp S)

= (05)(95) + (95)(05)

= 095

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 7) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store What is the probability that at least one cookie is stale

P(at least one) = P(S amp SC) or P(SC amp S) or (S amp S)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 7 revisited) A certain brand of cookies are stale 5 of the time You randomly pick a package of two such cookies off the shelf of a store

What is the probability that at least cookie is stale

P(at least one) = 1 ndash P(SC amp SC)

0975

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Ex 8) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Warm UpFemale Male Total

Allergies 10 8 18No Allergies

13 9 22

Total 23 17 40

Allergies

1 What is the probability of not having allergies

2 What is the probability of having allergies if you are a male

3 Are the events ldquoFemalerdquo and ldquoallergiesrdquo independent Justify your answer

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Handedness

Female Male Total

Left 3 1 __Right 18 8 __Total __ __ __

1 Are the events ldquofemalerdquo and ldquoright handedrdquo independent

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

What is the probability that a randomly selected resident who reads USA Today also reads the New York Times

There is a 125 chance that a randomly selected resident who reads USA Today also reads the New York Times

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

When performing a random simulation we can use Table D

Lets say I have a 30 Chance of winning a class lottery

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is a student

359195

)( StudentP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Whiteboard Challenge

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

The probability of any outcome of a random phenomenon is

(a) the precise degree of randomness present in the phenomenon

(b) any number as long as it is greater than 0 and less than 1

(c) either 0 or 1 depending on whether or not the phenomenon can actually occur or not

(d) the proportion of times the outcome occurs in a very long series of repetitions

(e) none of the above

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

A randomly selected student is asked to respond Yes No or

Maybe to the question ldquoDo you intend to vote in the next

presidential electionrdquo The sample space is Yes No Maybe

Which of the following represents a legitimate assignment of

probabilities for this sample space

(a)04 04 02

(b) 04 06 04

(c) 03 03 03

(d) 05 03 ndash02

(e) 1frasl4 1frasl4 1frasl4

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

You play tennis regularly with a friend and from past

experience you believe that the outcome of each

match is independent For any given match you have

a probability of 06 of winning The probability that

you win the next two matches is

(a) 016

(b) 036

(c) 04

(d) 06

(e) 12

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

There are 10 red marbles and 8 green marbles in a jar If you take three marbles from the jar (without replacement) the probability that they are all red is

(a) 0069(b) 0088 (c) 0147 (d) 0171 (e) 0444

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Jolor and Mi Sun are applying for summer jobs at a local restaurant After interviewing them the restaurant owner says ldquoThe probability that I hire Jolor is 07 and the probability that I hire Mi Sun is 04 The probability that I hire at least one of you is 09rdquo What is the probability that both Jolor and Mi Sun get hired

(a) 01 (b) 02 (c) 028 (d) 03 (e) 11

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

Select a random integer from ndash100 to 100 Which of the following pairs of events are mutually exclusive (disjoint)

(a) A the number is odd B the number is 5(b) A the number is even B the number is greater than 10 (c) A the number is less than 5 B the number is negative (d) A the number is above 50 B the number is less than 20 (e) A the number is positive B the number is odd

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

The probability of a ldquoYesrdquo answer given that the person was Female is

(a) 008

(b) 016

(c) 020

(d) 040

(e) 042

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

A recent survey asked 100 randomly selected adult Americans if they

thought that women should be allowed to go into combat situations

Here are the results classified by the gender of the subject

Gender Yes No

Male 32 18

Female 8 42

______________________________________________The probability that a randomly selected subject in the study is Male or answered ldquoNordquo is (a) 018 (b) 036 (c) 068 (d) 092 (e) 110

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

Describe what the Law of Large

Numbers says in the context of this

probability

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

An airline estimates that the probability that a

random call to their reservation phone line

result in a reservation being made is 031 This

can be expressed as P(call results in

reservation) = 031 Assume each call is

independent of other calls

What is the probability that none of the

next four calls results in a reservation

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 031 This can be expressed as P(call results in reservation) = 031 Assume each call is independent of other calls

You want to estimate the probability that exactly one of the next four calls result in a reservation being made Describe the design of a simulation to estimate this probability Explain clearly how you will use the partial table of random digits below to carry out five simulations

188 87370 88099 89695 87633 76987 85503 26257 51736189 88296 95670 74932 65317 93848 43988 47597 83044 190 79485 92200 99401 54473 190 34336 82786 05457 60343 191 40830 24979 23333 37619 56227 95941 59494 86539 192 32006 76302 81221 00693 95197 75044 46596 11628

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62

• Notes
• Sample Space
• Relative Frequency
• The Law of Large Numbers
• Event
• Complement
• Mutually Exclusive (disjoint)
• Not -Mutually Exclusive (Non- disjoint)
• UnionmdashDisjoint
• Slide 11
• Intersection
• Slide 13
• UnionmdashNot Disjoint
• Venn Diagrams
• Venn Diagram Mutually Exclusive Disjoint events
• Slide 17
• Venn diagram - Complement of A
• Venn diagram - A and B
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Basic Rules of Probability
• Slide 25
• Slide 26
• Slide 27
• Independent
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35
• Slide 36
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Slide 41
• Slide 42
• Conditional Probability and Independence
• Rule 7 Conditional Probability
• Slide 45
• Using Table Dhellip
• Probabilities from two way tables
• Slide 48
• Slide 49
• Slide 50
• Slide 51
• Slide 52
• Slide 53
• Slide 54
• Slide 55
• Slide 56
• Slide 57
• Slide 58
• Slide 59
• Slide 60
• Slide 61
• Slide 62