1. Pearson Unit 6 Topic 15: Probability 15-5: Conditional Probability With Frequency Tables Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

2. TEKS Focus:
(13)(D) Apply conditional probability in contextual problems.
(1)(E) Create and use representations to organize, record, and communicate mathematical ideas.
(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.

3. DEFINITIONS: Definition Picture or Example Two-Way Frequency Table
A table that displays the frequencies of data in two different categories.
A table with number of boys and girls that attend two different schools.
Contingency Table
Also known as a two-way frequency table. Displays the frequencies of data in two different categories.
A table that displays the number of two kinds of dogs seen at 2 different parks.
Conditional Probability
The probability that an event will occur, given that another event has already occurred.
Randomly choosing a sophomore from a group of students that don’t play sports.

4. Example 1:
The table below shows the number of students who passed their driving test as well as whether they took a driver’s education class to prepare.
How many students took the driving test? ______
How many passed the driving test?
______
How many students took the Driver’s Education class? _____
What percentage of the students that took the class passed the drivers test? _____ 80 50 39
32/39 ≈ 82%

5. Example 1 continued: 41 18/41 ≈ 44%
How many students did not take the Driver’s Education class? ____
What percentage of the students that didn’t take the class passed the driver’s test? Round the answer to the nearest percent. ______
What effect, if any does taking the Driver’s Education class have on passing the driver’s test? 41
18/41 ≈ 44%
Students who took the class were more likely to pass their test.

6. Example 2:
The table below shows data about student involvement in extracurricular activities at school. What is the probability that a randomly chosen student is a female not involved in extracurricular activities? Round the answer to the nearest tenth of a percent.
Relative frequency = females not involved = 120 ≈ 0.233
Total # of students
The probability is ≈ 23.3%

7. Example 3:
The two-way frequency table shows the number of male and female students by grade level on the prom committee. What is the probability that a member of the prom committee is a male who is a junior? Give the final answer as a %.
P(male junior/prom committe) = = .25 = 25% 12

8. Example 4:
Respondents of a poll were asked whether they were for, against, or had no opinion about a bill before the state legislature that would increase the minimum wage. What is the probability that a randomly selected person is over 60 years old, given that the person had no opinion on the state bill?
P (over 60/no opinion) = 40
100
= 40%

9. Example 5:
What is the probability that a randomly selected person is years old, given that the person is in favor of the minimum-wage bill? Round the answer to the nearest tenth of a percent.
P(30-45 yrs/favor of bill) = ≈ ≈ 25.6%
780

10. Example 6:
What is the probability that a randomly selected person is NOT old, given that the person is in favor of the minimum-wage bill? Round to the nearest tenth.
P(NOT yrs/favor of bill) = = 470 ≈ ≈ 60.3%

11. EXAMPLE 7:
Verizon has 150 sales representative in the San Antonio area. Two months after a sales seminar, Verizon’s vice president made a table of relative frequencies based on the sales results. What is the probability that someone who attended the seminar had an increase in sales?
P(increased sales/attended seminar) = = 0.6 = 60%
0.8

12. EXAMPLE 8:
Verizon has 150 sales representative in the San Antonio area. What is the probability that a randomly selected sales representative, who did not attend the seminar, did not see an increase in sales?
P(no sales/did not attended seminar) = = 0.9 = 90%
0.2

13. EXAMPLE 9: 8 12 24 26 (.4)(20) = 8 females that attended school play
20 – 8 = 12 females who did not attend the play
= 24 females attended the play
= 26 that did not attend the play; or 50 – 24 = 26 that did not attend the play 8 12 24 26