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

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.

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.

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%

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.

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 516 The probability is ≈ 23.3%

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) = 3 = .25 = 25% 12

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%

Example 5: What is the probability that a randomly selected person is 30-45 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) = 200 ≈ 0.256 ≈ 25.6% 780

Example 6: What is the probability that a randomly selected person is NOT 18-29 old, given that the person is in favor of the minimum-wage bill? Round to the nearest tenth. P(NOT 18-29 yrs/favor of bill) = 780-310 = 470 ≈ 0.603 ≈ 60.3% 780 780

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) = 0.48 = 0.6 = 60% 0.8

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) = 0.18 = 0.9 = 90% 0.2

EXAMPLE 9: 8 12 24 26 (.4)(20) = 8 females that attended school play 20 – 8 = 12 females who did not attend the play 16 + 8 = 24 females attended the play 14 + 12 = 26 that did not attend the play; or 50 – 24 = 26 that did not attend the play 8 12 24 26