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Objective
Find the probability of independent and
dependent events
Vocabulary
Compound Event
An event that consists of two or more simple
events
Vocabulary
Independent Events
Two or more events in which the outcome of
one event does not affect the outcome of the
other event(s)
Vocabulary
Dependent events
Two or more events in which the outcome of
one event does affect the outcome of the other
event(s)
Example 1 Probability of Independent Events
Example 2 Use Probability to Solve a Problem
Example 3 Probability of Dependent Events
The two spinners below are spun. What is the probability
that both spinners will show a number greater than 6?
6
Writethan
probability
statement
P(greater than 6) = Numbers greater
Total Numbers
for the 1st spinner
Write the formula for
probability
1/3
The two spinners below are spun. What is the probability
that both spinners will show a number greater than 6?
P(greater than 6) = Numbers greater than 6
Total Numbers
P(greater than 6) = 3
Count the numbers greater
than 6 for the numerator
1/3
The two spinners below are spun. What is the probability
that both spinners will show a number greater than 6?
P(greater than 6) = Numbers greater than 6
Total Numbers
P(greater than 6) = 3
10
Count the total numbers for
the denominator
1/3
The two spinners below are spun. What is the probability
that both spinners will show a number greater than 6?
P(greater than 6) = 3
10
P(greater than 6) = 3
10
The second spinner is exactly
like the 1st spinner except for
color so same probability
1/3
The two spinners below are spun. What is the probability
that both spinners will show a number greater than 6?
P(greater than 6) = 3
10
Write the probability
statement for both spinners
P(greater than 6) = 3
10
Multiply the probability of
each spinner
P(both spinners greater than 6) = 3  3
10
10
Answer:
P(both spinners greater than 6) = 9
100
NOTE: Independent event since neither
Use calculator to multiply
spinner affected the other
1/3
The two spinners below are spun. What is the probability
that both spinners will show a number less than 4?
Answer: P (both spinners less than 4) =
1/3
Cross River Middle School
What is the probability that a
student picked at random will
be an eighth-grade girl?
Demographic
Group
Fraction of the
Population
Grade 6
Grade 7
P(8th grade girl) =
Grade 8
Boys
Girls
Write probability statement
for an eighth-grade girl
2/3
Cross River Middle School
What is the probability that a
student picked at random will
be an eighth-grade girl?
Demographic
Group
Fraction of the
Population
Grade 6
Grade 7
P(8th grade girl) =
Grade 8
Boys
Girls
Note: Data is given in
fractions which can be
used as a probability!
2/3
Cross River Middle School
What is the probability that a
student picked at random will
be an eighth-grade girl?
Demographic
Group
Fraction of the
Population
Grade 6
Grade 7
P(8th grade girl) =

Grade 8
Boys
Girls
Write probability of 8th grade
Put multiplication sign
Write probability of girl
2/3
Cross River Middle School
What is the probability that a
student picked at random will
be an eighth-grade girl?
Demographic
Group
Grade 6
Grade 7
P(8th grade girl) =
Answer:
P(8th grade girl) =

Grade 8
Boys
Girls
Multiply
NOTE: Independent event since neither
probability affected the other probability
2/3
Fraction of the
Population
POPULATION Use the information below. What is the
probability that a student picked at random will be a
sixth grade boy?
Monterey Middle School
Demographic
Group
Answer:
Probability (6th grade boy) =
Grade 6
Grade 7
Grade 8
Boys
Girls
2/3
Fraction of the
Population
There are 4 red, 8 yellow, and 6 blue socks in a drawer.
Once a sock is selected, it is not replaced. Find the
probability that two blue socks are chosen.
This is a dependent event
P(1st sock blue) =
Since the sock is not put
back, it will affect the
probability of the second
sock chosen
Write probability statement
for the first sock chosen
3/3
There are 4 red, 8 yellow, and 6 blue socks in a drawer.
Once a sock is selected, it is not replaced. Find the
probability that two blue socks are chosen.
This is a dependent event
P(1st sock blue) = 6
18
Numerator is number of
blue socks
Denominator is total
number of socks in drawer
3/3
There are 4 red, 8 yellow, and 6 blue socks in a drawer.
Once a sock is selected, it is not replaced. Find the
probability that two blue socks are chosen.
This is a dependent event
P(1st sock blue) = 6
18
P(2nd sock blue) =
5
17
Write probability statement
for the second sock chosen
Numerator is number of
blue socks minus the one
not replaced
Denominator is total
number of socks in drawer
minus the one not replaced
3/3
There are 4 red, 8 yellow, and 6 blue socks in a drawer.
Once a sock is selected, it is not replaced. Find the
probability that two blue socks are chosen.
This is a dependent event
P(1st sock blue) = 6
18
P(2nd sock blue) =
5
17
P(both socks blue) =
Write probability statement
for both socks
Multiply the two
probabilities of the 2 socks
chosen
Multiply
Answer:
P(both socks blue) =
3/3
*
There are 6 green, 9 purple, and 3 orange marbles in a
bag. Once a marble is selected, it is not replaced.
Find the probability that two purple marbles are
chosen.
Answer: P (two purple marbles) =
3/3
Assignment
Lesson 8:5
Probability of Compound
Events
4 - 26 All