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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
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
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-
Helpful websites
httpwwwmathgoodiescomlessonsvol6conditionalhtml
httpbrightstormcommathalgebra-2combinatoricsintroduction-to-probability
- Probability
- Review
- Mutually Exclusive Events
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
-