Transcript Independent and Dependent Events

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Objective
Find the probability of
independent and dependent events
Vocabulary
Compound event
An event consisting of two or more simple events
Vocabulary
Independent event
Two or more events in which the outcome of one
event does not affect the outcome of the other
event(s)
Vocabulary
Dependent event
Two or more events in which the outcome of one
event affects the outcome of the other event(s)
Example 1 Independent Events
Example 2 Dependent Events
LUNCH For lunch, Jessica may choose from a turkey
sandwich, a tuna sandwich, a salad, or a soup. For a
drink, she can choose juice, milk, or water. If she
chooses a lunch at random, what is the probability that
she chooses a sandwich (of either kind) and juice?
P(sandwich) =
2
4
Write probability statement
for the meal
There are 2 choices for a
sandwich - turkey and tuna
There are 4 total choices
for a meal
1/2
LUNCH For lunch, Jessica may choose from a turkey
sandwich, a tuna sandwich, a salad, or a soup. For a
drink, she can choose juice, milk, or water. If she
chooses a lunch at random, what is the probability that
she chooses a sandwich (of either kind) and juice?
P(sandwich) =
22
4 2
1
P(sandwich) =
2
Find the GCF = 2
Divide GCF into numerator
and denominator
1/2
LUNCH For lunch, Jessica may choose from a turkey
sandwich, a tuna sandwich, a salad, or a soup. For a
drink, she can choose juice, milk, or water. If she
chooses a lunch at random, what is the probability that
she chooses a sandwich (of either kind) and juice?
1
P(sandwich) = 2
P(juice) =
1
3
Write probability statement
for the drink
There is 1 choice for a juice
There are 3 choices for a
drink
Numerator is 1 so already
in simplest form
1/2
LUNCH For lunch, Jessica may choose from a turkey
sandwich, a tuna sandwich, a salad, or a soup. For a
drink, she can choose juice, milk, or water. If she
chooses a lunch at random, what is the probability that
she chooses a sandwich (of either kind) and juice?
1
P(sandwich) = 2
P(juice) = 1
3
Write probability statement
for a sandwich AND juice
P(sandwich AND juice) = 1  1
3
2
Multiply probability of
sandwich and juice
1/2
LUNCH For lunch, Jessica may choose from a turkey
sandwich, a tuna sandwich, a salad, or a soup. For a
drink, she can choose juice, milk, or water. If she
chooses a lunch at random, what is the probability that
she chooses a sandwich (of either kind) and juice?
1
P(sandwich) = 2
P(juice) = 1
3
P(sandwich AND juice) = 1  1
3
2
Answer:
1
P(sandwich AND juice) =
6
Multiply
NOTE: This is an
independent event
because neither
probability affected the
other
1/2
SWEATS Zachary has a blue, a red, a gray, and a
white sweatshirt. He also has blue, red, and gray
sweatpants. If Zachary randomly pulls a sweatshirt
and a pair of sweatpants from his drawer, what is the
probability that they will both be blue?
Answer: P(blue sweatshirt, blue sweatpants) =
NOTE: This is an independent event
1/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
15
P(girl’s name) =
27
Write probability statement
for the meal
There are 15 girls
There is a total of 15 girls
and 12 boys = 27 students
2/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
P(girl’s name) =
15  3
27  3
5
P(girl’s name) =
9
Find the GCF = 3
Divide GCF into numerator
and denominator
2/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
P(girl’s name) = 5
9
Write probability statement
for boy’s name
12
P(boy’s name) =
26
There are 12 boys
NOTE: This is a dependent
event because the first
probability affects the second
There is a total of 15 girls
and 12 boys = 27 students
1 name has already been
used so 27 - 1 = 26 students
2/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
P(girl’s name) = 5
9
Find the GCF = 2
12  2
P(boy’s name) =
26  2
Divide GCF into numerator
and denominator
P(boy’s name) = 6
13
2/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
Write probability statement
for a girl first, then boy
P(girl’s name) = 5
9
6
P(boy’s name) =
13
P(girl first, then boy) =
Multiply probability of girl’s
name and boy’s name
5 6
9 13
2/2
COMMITTEE SELECTION Mrs. Tierney will select two
students from her class to be on the principal’s
committee. She places the name of each student in a
bag and selects one at a time. The class contains 15
girls and 12 boys. What is the probability she selects a
girl’s name first, then a boy’s name?
P(girl first, then boy) = 5  6
9 13
30  3
P(girl first, then boy) =
117  3
Answer:
P(girl first, then boy) = 10
39
Multiply
Find the GCF = 3
Divide GCF into
numerator and
denominator
2/2
*
DOUGHNUTS A box of doughnuts contains 15 glazed
doughnuts and 9 jelly doughnuts. Jennifer selects
two doughnuts, one at a time. What is the probability
that she selects a jelly doughnut first, then a glazed
doughnut?
Answer: P(jelly, then glazed) =
2/2
Lesson 9:7
Assignment
Independent and Dependent
Events
4 - 16 All