Lesson 49
Mr. Jones
Trigonometry
Name:_______________________
Date:___________________
S.W. B. A. T: Identify and find conditional relative frequencies. Use conditional
relative frequencies to find conditional probability.
DO NOW:
Cameron surveys students in his school who play sports, and asks them which sport they
prefer. He records the responses in the table below.
a) How many students play sports? What is that number called?
b) What is the joint frequency for male students who prefer soccer?
c) What is the marginal frequency for each type of sport?
d) What is the joint relative frequency for a female playing baseball?
Definitions
Relative frequency is the interval frequency, f, divided by the total frequency, n.
Relative frequency =
𝑓
𝑛
=
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
Two-way frequency table (also called a contingency table) is a frequency table that displays
data that belongs to two different categories. For instance, a table can show the leisure
activities of adults.
Joint frequency is the entries in the body of the two-way frequency table.
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Joint relative frequency is the ratio of a frequency that is not in the total row or the total
column to the total number of values or observations.
Marginal frequency is the entry in the “total” for the column and the “total” for the row in
two-way frequency table.
Marginal relative frequency is the sum of the joint relative frequencies in a row or column.
Conditional frequency is when the body of two-way table contains relative frequencies.
Conditional relative frequency is the ratio of a joint relative frequency to the marginal
relative frequency.
Example 1: Juniors and seniors were asked if they plan to attend college right after graduation, seek fulltime employment, or some other option. A random sample of 100 students was selected from those who co
mpleted the survey. Scott started to calculate the relative frequencies to the nearest hundredth. Complete the
table.
Complete the table below to find the conditional relative frequencies for the data above.
Plan to attend Plan to seek full Other
college
time
options
employment
Totals
Seniors
Juniors
Totals
2
Exercise 1: Find the conditional relative frequency.
Conditional Frequency illustrating the preferences for sports and videos game broken down
by gender.
Sports
Video Games
Total
Male
students
0.304
0.348
0.652
Female
students
Total
0.261
0.087
0.348
0.565
0.435
1.00
Conditional relative frequency by each rows two-way table.
Sports
Video Games
Total
Male
students
Female
students
Total
3
Example 2: Suppose you randomly survey the juniors and seniors about whether they are
attending a school concert. The joint relative frequencies are below.
Attending
Not Attending
Total
Juniors
0.191
0.291
0.482
Seniors
0.350
0.168
0.518
Total
0.541
0.459
1.000
a) What is the probability that a randomly selected junior will be attending the concert?
b) What is the probability that a student not attending the concert is a senior?
Exercise 2: Three different local hospitals in New York surveyed their patients. The survey
asked whether the patient’s physician communicated efficiently. The results, given as joint
relative frequencies, are shown below.
Glen Falls
Saratoga
Albany
Yes
0.123
0.288
0.338
NO
0.042
0.077
0.131
a) What is the probability that a randomly selected patient located in Saratoga was
satisfied with the communication of the physician?
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b) What is the probability that a randomly selected patient who not satisfied with the
physician’s communication is located in Glen Falls?
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EXIT
1. Complete joint relative frequency table.
Sports
Male
students
Female
students
Total
0.261
Video Games
Total
0.348
0.652
0.087
0.435
1.00
Complete conditional relative frequency table
Sports
Video Games
Male
students
Female
students
c) What is probability that a randomly selected male students will prefer video games?
2. f(t) = sin t + cos t, find f(π)
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Lesson 49
Mr. Jones
Homework
Trigonometry
Name:_______________________
Date:___________________
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