probability what’s the chance of that happening? mm1d2 a, b, c

Probability

Whatrsquos the chance of that happening

MM1D2 a b c

ReviewEvent

One or

more

outcomes

OutcomeThe result of a single trial of an experiment

ProbabilityThe

measure of

how likely

an event is

(between 0

and 1)

Mutually Exclusive Events

Two events are said to be mutually

exclusive if they have no common

outcomes

Can even be odd

For example1Drawing an 8 or a king from a

standard deck of playing cards

2 Given a 6-sided number cube (a die) the event of rolling an even or an odd number

Possibilitiesyou draw an 8you draw a

king

Possibilitiesyou roll an evenyou roll an odd

Non-mutually Exclusive Events (Inclusive Events)

Events that have common

outcomes

Can you draw a queen that is also a spade

For example1 Rolling a 6-sided die and getting a 5 or

an odd number

2 Drawing a heart or a king

Possibilitiesyou can roll a 5you can roll an odd numberyou can roll an odd number that is also 5

Possibilitiesyou can draw a heartyou can draw a kingyou can draw a king that is also a heart

Rule for Mutually Exclusive

P(A or B) = P(A) + P(B)

Probability of Mutually Exclusive Events

For example1 What is the probability of drawing

a 6 or a queen from a standard deck of

playing cards

Solution

13

2

52

8

52

4

52

4

QueenP 6P Queenor 6P

Rule for Non-mutually exclusiveP(A or B) = P(A) + P(B) ndash P(A and B)

Probability of Non-mutually Exclusive Events

For example1What is the probability you will

draw a diamond or a 2 from a standard deck of playing cards

Solution

13

4

52

16

52

1

52

4

52

13

2 and diamondP 2P diamondP or two diamondP

Helpful websites

httpwwwmathgoodiescomlessonsvol6intro_probabilityhtml

httprchsbowmanwordpresscom20091006statistics-notes-E28094-probability-rules-compound-events-mutually-exclusive-and-non-mutually-exclusive-events-addition-rule

httpbrightstormcommathalgebra-2combinatoricsprobability-of-multiple-events

Now go practice

Independent Events

Two events are independent

if the outcome of the first

event does not impact the

outcome of the second

eventRolling a die

Tossing a coin

Rule for independent events

P(A and B) = P(A) P(B)For example1 There are 6 red 4 green 8 black

and 10 yellow marbles in a jar You reach into the jar without looking and take out a marble You replace the marble you took out and you take a second marble What is the probability that the first marble is red and the second marble is yellow

Solution

yellow) and P(red P(yellow)P(red)

196

15

784

60

28

10

28

6

Dependent Events

Two events are dependent if

the outcome of the first affects

the outcome of the second

Irsquom not putting back my ace

Rule for dependent eventsP(A and B) = P(A) P(B|A)

adjust the outcomes for B

For example1 There are 6 red 4 green 8 black

and 10 yellow marbles in a jar You reach into the jar without looking and take out a marble You do not replace the marble you took out and you take a second marble What is the probability that the first marble is red and the second marble is yellow

Solution

yellow) and P(red P(yellow)P(red)

63

5

756

60

27

10

28

6

Notice the adjustment to the

outcomes

Conditional Probability

The probability event B

occurs given event A has

happened

Whatrsquos the chance I get an ace if I know one ace has been dealt

Rule for Conditional Probability

P(B | A) = P(A)

B) andP(A

For example1 A science teacher gives her class

two quizzes 25 of the students passed both quizzes and 42 of the students passed the first quiz What is the probability that a student passed the second quiz given they passed the first quiz

Helpful websites

httpwwwmathgoodiescomlessonsvol6conditionalhtml

httpbrightstormcommathalgebra-2combinatoricsintroduction-to-probability