1. Chapter 5 Probability 5.2A Addition Rule

2. Addition Rule (General Rule) If we have two events A and B, then: P(A or B) = P(A) + P(B) – P(A & B)

3. Why subtract P(A and B) P(A or B) A B A and B

4. Why subtract P(A and B) P(A) A B

5. Why subtract P(A and B) P(B) A B

6. Why subtract P(A and B) P(A and B) is in there twice!!! We subtract so it is only in there once! A B A and B

7. Mutually Exclusive: If events A and B cannot occur at the same time, then they are mutually exclusive or disjoint events. *If two events A and B are disjoint or mutually exclusive, then P(A and B)=0

8. Venn diagram – Mutually Exclusive Events A B A B In this case there is no intersection. Since P(A and B) = 0, we do not have to subtract.

9. Example #1 Events that are mutually exclusive when we roll a single die: 1.Rolling a 5 and a 2 2.Rolling an even number and an odd number 3.Getting a number greater than 4 and a number less than 2

10. Events that are not mutually exclusive when we roll a single die: 1.Rolling a 3 and an odd number 2.Rolling an even number and a number greater than 4. 3.Rolling a multiple of 3 and an even number.

11. Try These Example #2 Determine whether the events listed are mutually exclusive or not mutually exclusive when selecting cars from the Dorman High School Parking Lot: a.Selecting a white car and an SUV. b.Selecting a car with a V6 engine and a car with a V8 engine.

12. Try These Determine whether the events listed are mutually exclusive or not mutually exclusive when selecting cars from the Dorman High School Parking Lot: c.Selecting a Chevrolet and a Ford d.Selecting a car that is a 2002 model and a truck

13. a.Selecting a white car and an SUV. NME b.Selecting a car with a V6 engine and a car with a V8 engine. ME c.Selecting a Chevrolet and a Ford ME d.Selecting a car that is a 2002 model and a truck NME

14. Addition Rule (Reminder) (General Rule) If we have two events A and B, then: P(A or B) = P(A) + P(B) – P(A & B) Now we will learn how to use the Addition Rule!!

15. Example #3 Suppose there are 23 professors at a small college. Of these, 8 teach Math, 8 teach English, 7 teach Science and 6 teach social sciences. We also know that 4 teach Math and Science and 2 teach English and Social Science. We randomly select a professor. Find the following probabilities:

16. a.The professor teaches Math or Social Science b.The professor teaches English or Science ME?

17. c.The professor teaches Math or Science d.The professor teaches English or Social Science ME?

18. Example #4 A pizza buffet is almost out of pizza and only has 27 pieces of pizza left. 16 of these are hamburger, 7 are pepperoni and 4 are cheese. 17 are thin crust and 10 are thick crust. 10 of the Hamburger are thin crust and 6 are thick crust. All 7 pepperoni are thin crust and all 4 cheese are thick crust. If a piece of pizza is selected at random, find the probability that it is:

19. a.Pepperoni or Hamburger b.Cheese or Thick Crust ME?

20. c.Hamburger or Thin Crust d.Pepperoni or Thick Crust ME?

21. Example #5 Musical styles other than rock and pop are becoming more popular. A survey of college students finds that the probability they like country music is.40. The probability that they liked jazz is.30 and that they liked both is.10. What is the probability that they like country or jazz? P(C or J) =.4 +.3 -.1 =.6

22. Probabilities from two way tables Example #6 StuStaffTotal American107105212 European331245 Asian5547102 Total195164359 a) What is the probability that the driver is a student?

23. Probabilities from two way tables StuStaffTotal American107105212 European331245 Asian5547102 Total195164359 b) What is the probability that the driver drives an American or Asian car? ME?

24. Probabilities from two way tables StuStaffTotal American107105212 European331245 Asian5547102 Total195164359 c) What is the probability that the driver is staff or drives an Asian car? ME?

25. Probabilities from two way tables StuStaffTotal American107105212 European331245 Asian5547102 Total195164359 d) What is the probability that the driver is student or drives an American car? ME?

26. Example #7: A certain ophthalmic trait is associated with eye color. See table below: BlueBrownOtherTotal Trait Present703020120 Not Present2011050180 Total9014070300 a) What is the probability that the trait is present? ME?

27. Example #7: A certain ophthalmic trait is associated with eye color. See table below: BlueBrownOtherTotal Trait Present703020120 Not Present2011050180 Total9014070300 b) What is the probability that the trait is not present or the person has blue eyes? ME?

28. Example #7: A certain ophthalmic trait is associated with eye color. See table below: BlueBrownOtherTotal Trait Present703020120 Not Present2011050180 Total9014070300 c) What is the probability that the trait is present or the person has brown eyes? ME?

29. Example #7: A certain ophthalmic trait is associated with eye color. See table below: BlueBrownOtherTotal Trait Present703020120 Not Present2011050180 Total9014070300 d) What is the probability that the person has blue or brown eyes? ME?