1. Probability Part 4 – “Or” Events

2. Probability Warm-up In a survey, 16 percent of American children said they use flattery to get their parents to buy them things. If a child is selected at random, find the probability that the child said he or she does not use parental flattery.

3. Probability Agenda Warm-up Homework Review Objective: To understand and apply the rules of probability associated with “or” events Summary Homework

4. Probability “Or” events – These involve situations in which more that one outcome is desirable. Example- Drawing a diamond or a heart from a deck of cards. The can be either mutually exclusive (disjoint) events or non-mutually exclusive (non-disjoint) events) This is the idea of cumulative probability- it adds together.

5. BPS - 5th Ed.Chapter 125 Addition Rule: for Disjoint Events P(A or B) = P(A) + P(B)

6. BPS - 5th Ed.Chapter 126 General Addition Rule P(A or B) = P(A) + P(B)  P(A and B)

7. Example 1 You have 10 marbles in a bag – 5 blue, 3 green and 2 red. What is the probability of drawing a red or a green marble? P(R or G) = P(R) + P(G) P(R or G) = 2/10 + 3/10 = 5/10 or.5

8. Example 2 You have the following distribution: ElementaryHigh SchoolTotal Women9546141 Men85361 Total10399202

9. Example 2 What is the probability of drawing a name at random and it is that of a woman? 141/202 What is the probability of drawing a name at random and it is that of a high school teacher? 99/202 What is the probability of drawing a name at random and it is that of a woman or a high school teacher? 194/202 or 97/101

10. BPS - 5th Ed.Chapter 1210 Example 3 Student Demographics At a certain university, 80% of the students were in- state students (event A), 30% of the students were part- time students (event B), and 20% of the students were both in-state and part-time students (event {A and B}). So we have that P(A) = 0.80, P(B) = 0.30, and P(A and B) = 0.20. What is the probability that a student is either an in- state student or a part-time student?

11. BPS - 5th Ed.Chapter 1211 Other Students P(A or B)= P(A) + P(B)  P(A and B) = 0.80 + 0.30  0.20 = 0.90 All Students Part-time (B) 0.30 {A and B} 0.20 Example 3 In-state (A) 0.80

12. BPS - 5th Ed.Chapter 1212 Other Students All Students Part-time (B) 0.30 Example 3 {A and B} 0.20 In-state (A) 0.80 In-state, but not part-time (A but not B): 0.80  0.20 = 0.60

13. Probability 1) Determine which events are mutually exclusive and which are not, when a single die is rolled. a. Getting an odd number and getting an even number b. Getting a 3 and getting an odd number c. Getting an odd number and getting a number less than 4 d. Getting a number greater than 4 and getting a number less than 4 2) At a political rally, there are 20 Republicans, 13 Democrats, and 6 Independents. If a person is selected at random, find the probability that he or she is either a Democrat or an Independent. In a hospital unit there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. If a staff person is selected, find the probability that the subject is a nurse or a male.

14. Probability Summary

15. Probability Homework Probability Practice 4