COAL B
Notes on Conditional Frequencies
Name _________________________
Warm up The table shows the number of books sold at a library sale. Complete the table with the joint
and marginal relative frequencies.
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If given:
then
Joint Relative Frequencies
are the values in each
category divided by the
total number of values.
Marginal Relative Frequencies
are found by adding the joint
relative frequencies in each
row and column.
-------------------------------------------------------------------------------------------------------------------------------------------------Conditional Relative Frequency To find a conditional relative frequency, divide the joint relative
frequency by the marginal relative frequency. Conditional relative frequencies can be used to find
conditional probabilities (the likelihood of something occurring).
Note: Joint/Marginal (its will ALWAYS be less than 1)
--------------------------------------------------------------------------------------------------------------------How to use Conditional Relative Frequency to Find Probability:
A sociologist collected data on the types of pets in 100 randomly selected households, and summarized
the results in a table.
1. If you are given that a household has a dog, what is the probability that the household also has a cat?
2. If you are given that a household does not have a cat, what is the probability that the household also
does not have a dog?
The classes at a dance academy include ballet
and tap dancing. Enrollment in these classes
is shown in the table.
Complete the table of the joint relative
frequencies and marginal relative frequencies
3. Given that a student is taking ballet, what is the probability that the student is not taking tap?
4. Given that a student is not taking ballet, what is the probability that the student is taking tap?
-------------------------------------------------------------------------------------------------------------------------------------------------Tomas is trying to decided on the best possible route to drive to work. Each day he recorded how often
he was late or on-time on each route. The corresponding table of joint and marginal relative frequencies
is below:
What is the probability of being late given Route A?
What is the probability of being late given Route B?
What is P(being late if driving Route C)?
Probability of being late is least on route ______.
Classwork/Homework
1. The table shows the joint and marginal relative frequency results of a poll of randomly selected high
school students who were asked if they prefer to hear all-school announcements in the morning or
afternoon.
Underclassmen
Morning
0.16
Afternoon 0.36
Total
0.52
Upperclassmen
0.28
0.2
0.48
Total
0.44
0.56
1
a. What percent of the students are underclassmen?
b. Given the student is an upperclassman, what is the probability the student prefer to hear the
announcements in the afternoon?
c. Of the students who prefer to hear the announcements in the afternoon, what percent are
upperclassmen?
d. What percent of the students prefer morning announcements?
Classwork/Homework Continued
Name ________________________
3. The table shows the joint and marginal relative frequency results of a customer satisfaction survey
for a cellular service provider, by location of the customer. In the survey, customers were asked
whether they would recommend a plan with the provider to a friend. Round to the nearest hundredth
where appropriate.
Arlington
Yes
0.27
No
0.12
Total 0.39
Towson
0.23
0.07
0.3
Parkville
0.27
0.04
0.31
Total
0.77
0.23
1
a. Of the customers who are from Parkville, what percent would recommend a plan with the cellular
provider?
b. What percent of the customers who said no are from Towson?
c. CHALLENGE: Given the customer answered yes, what percent of them were from Towson or
Arlington?
Classwork/Homework Continued
Name ________________________
3. The table shows the joint and marginal relative frequency results of a customer satisfaction survey
for a cellular service provider, by location of the customer. In the survey, customers were asked
whether they would recommend a plan with the provider to a friend. Round to the nearest hundredth
where appropriate.
Arlington
Yes
0.27
No
0.12
Total 0.39
Towson
0.23
0.07
0.3
Parkville
0.27
0.04
0.31
Total
0.77
0.23
1
a. Of the customers who are from Parkville, what percent would recommend a plan with the cellular
provider?
b. What percent of the customers who said no are from Towson?
c. CHALLENGE: Given the customer answered yes, what percent of them were from Towson or
Arlington?