1. Conditional Probability Honors

2. Conditional Probability  The probability of an event occurring, given that another event has already occurred  Denoted P(B | A) (read “probability of B, given A”)  (probability of event B occuring, given that event A has occurred)

3.  Two Way Frequency Table  A frequency table that contains data from two different categories 3

4.  The table shows students by gender and by type of school in 2005. You pick a student at random. What is P(female | graduate school)? 4

5.  The table shows students by gender and by type of school in 2005. You pick a student at random. What is P(female)? 5

6.  Americans recycle increasing amounts through municipal waste collection. The table shows the collection data for 2007. What is the probability that a sample of recycled waste is paper? 6

7. Example A recent survey of 400 instructors at a major university revealed the data shown in the following table. Based on the data, what are the probabilities of the following? a. An instructor received a good evaluation, given the instructor was tenured. b. An instructor received a poor evaluation, given the instructor was tenured. 7

8. Solutions Status Good Evaluations Poor Evaluation s Tenured72168 Nontenured8476 8

9. Two cards are selected in sequence from a standard deck. Find the probability that the second card is a queen, given that the first card is a king. (Assume that the king is not replaced.) Solution: Because the first card is a king and is not replaced, the remaining deck has 51 cards, 4 of which are queens.

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11.  A utility company asked 50 of its customers whether they pay their bills online or by mail. What is the probability that a customer pays the bill online, given that the customer is a male? 11

12. Researchers asked people who exercise regularly whether they jog or walk. Fifty-eight percent of the respondents were male. Twenty percent of all respondents were males who said they jog. Find the probability that a male respondent jogs. Relate:P( male ) = 58% P( male and jogs ) = 20% Define:Let A = male. Let B = jogs. The probability that a male respondent jogs is about 34%. Write:P( A | B ) = P( A and B ) P( A ) = Substitute 0.2 for P(A and B) and 0.58 for P(A). 0.344Simplify. 0.2 0.58

13. From That P(A and B) = P(A) * P(B | A) 13

14.  A school system compiled the following information from a survey it sent to people who were juniors 10 years earlier. ◦ 85% of the students graduated from high school ◦ Of the students who graduated from high school, 90% are happy with present job ◦ Of the students who did not graduate from high school, 60% are happy with their present job. ◦ What is the probability that a person from the junior class 10 years ago graduated from high school and is happy with his/her present job? 14

15. ◦ 85% of the students graduated from high school ◦ Of the students who graduated from high school, 90% are happy with present job ◦ Of the students who did not graduate from high school, 60% are happy with their present job. ◦ What is the probability that a person from the junior class 10 years ago graduated from high school and is happy with his/her present job? 15

16. Two cards are selected, without replacing the first card, from a standard deck. Find the probability of selecting a king and then selecting a queen. Solution: Because the first card is not replaced, the events are dependent.

17. 1. Use the table to find each probability a. P(has diploma) b. P(has diploma and experience) c. P(has experience | has diploma) d. P(has no diploma | has experience) 2. Researchers asked shampoo users whether they apply shampoo directly to the head, or indirectly using a hand. What is the probability that a respondent applies shampoo directly to the head, given that the respondent is female? 3. Use the survey results a. Find the probability that a respondent has a pet, given the respondent has had a pet. b. Find the probability that a respondent has never had a pet given that the respondent does not have a pet now. 17