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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Helpful websites

httpwwwmathgoodiescomlessonsvol6conditionalhtml

httpbrightstormcommathalgebra-2combinatoricsintroduction-to-probability