The probable is what usually

happens. Aristotle

Chapter 6: Probability

Chance experiment: any activity or

situation in which there is uncertainty

about which outcome will result

Fate laughs at probabilities. Bulwer, Lytton E.G.

Sample Space: collection of all

possible outcomes of a chance experiment

Roll a dieS={1,2,3,4,5,6}

Probability is the very guide of life. Cicero

What is the sample space?

1.) Rolling 1 die

2.) Rolling 2 dice and counting the number of pips face up

3.) Toss a coin

4.) Toss a coin three times and record the results

5.) Flip a coin and roll a die

S = {1,2,3,4,5,6}

S = {2,3,4,5,6,7,8,9,10,11,12}

S = {H,T}

S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}

S = {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

An event is any collection of outcomes from the sample space of a chance experiment.

– Rolling a prime # E = {2,3,5}

A simple event is an event consisting of exactly one outcome.

Rolling a 6: E = {6}

Venn Diagrams•Used to display relationships

•between events

•Helpful in calculating probabilities

Complement •Consists of all outcomes that are not in the event

–Not rolling a even #EC={1,3,5}

The rectangle represents the sample space and shaded area represents the event A.

The shaded area represents the event not A.

Union •the event A or B happening•consists of all outcomes that are in at least one of the two events–Rolling a prime # or even number

E={2,3,4,5,6}

BAE

The shaded area represents the event

A or B ( the union of two events).

Union (or)

BAE

Intersection •the event A and B happening

•consists of all outcomes that are in both events–Drawing a red card and a “2” – E = {2 hearts, 2 diamonds}

BAE

Intersection (and)

The shaded area represents the event

A and B (the intersection of two sets).

BAE

Mutually Exclusive (disjoint)

•two events have no outcomes in common

–Roll a “2” or a “5”

• Two events that have no common outcomes are said to be disjoint or mutually exclusive.

A and B are disjoint events

Some illustrations

A B

C

A B C

A B

C

A, B & C are Disjoint

A B

C

A B C

A B

C

A B Cc

A ∩ B ∩ C

A υ B υ C A ∩ B ∩ Cc

Com Sci

Statistics & Computer Science & not Calculus

Stat Cal

Com Sci

Calculus or Computer Science

Stat Cal

Com Sci

(Statistics or Computer Science) and not Calculus

Stat Cal

Com Sci

Statistics and not (Computer Science or Calculus)

Stat Cal

Com Sci

Stat Cal

Com Sci

Statistics or Computer Science?

30 10520

1010

20

80

170

Stat Cal

Com Sci

Statistics and Computer Science?

30 10520

1010

20

80

20

Stat Cal

Com Sci

Statistics or (Computer Science and Calculus)?

30 20 105

10 20

80

10

90

Stat Cal

Com Sci

(Statistics or Computer Science) and Calculus?

30 20 105

10

10

20

80

50

Country-Western songs emphasize three basic themes: love, prison, and trucks. A survey of the local Country-Western radio station produced the following data: 12 songs about a truck driver who is in love while in prison2 about people in prison who are not in love and do not drive trucks8 about people who are out of prison, are not in love, and do not drive a truck13 about a prisoner in love28 about a person in love18 about a truck driver in love16 about truck drivers who are not in prison3 about a truck driver in prison who is not in love

12 songs about a truck driver who is in love while in prison2 about people in prison who are not in love and do not drive trucks8 about people who are out of prison, are not in love, and do not drive a truck13 about a prisoner in love28 about a person in love18 about a truck driver in love16 about truck drivers who are not in prison3 about a truck driver in prison who is not in love

How many songs were about:a.) truck drivers?

b.) prisoners?

c.) truck drivers in prison?

d.) people not in prison?

e.) people not in love?

f.) How many songs were surveyed?

Always be a little

improbable.Wilde, Oscar