Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B)

1. Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and Bboth occur at the same time. 4.3 Compound Event

2. Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and Bboth occur at the same time. Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome iscounted only once. P(A or B) is equal to that sum, divided by the total number of outcomes. 4.3 Compound Event

3. Events A and B are disjoint or mutually exclusive if they cannot occur simultaneously (at the same time). Definition

4. Events A and B are disjoint or mutually exclusive if they cannot occur simultaneously. Total Area = 1 P(A) P(B) P(A and B) Overlapping Events

5. Events A and B are disjoint or mutually exclusive if they cannot occur simultaneously. Total Area = 1 Total Area = 1 P(A) P(B) P(A) P(B) P(A and B) Overlapping Events Non-overlapping Events

6. Figure 3-7 Applying the Addition Rule P(A or B) Addition Rule Are A and B mutually exclusive ? Yes P(A or B) = P(A) + P(B) No P(A or B) = P(A)+ P(B) - P(A and B)

7. EXAMPLE: In a study of 82 young drivers ( under the age of 32), 39 were men who were ticketed, 11 were men who were not ticketed, 8 were women who were ticketed, and 24 were women who were not ticketed. If one of the subjects is randomly selected, find the probability of getting a woman or someone who was not ticketed.

8. EXAMPLE: Find the probability of randomly selecting a man or a boy. Contingency Table: Titanic Mortality April 15, 1912 Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223

9. Find the probability of randomly selecting a man or a boy. Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223

10. Find the probability of randomly selecting a man or a boy. P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223

11. Find the probability of randomly selecting a man or a boy. P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 * Mutually Exclusive *

12. EXAMPLE: Find the probability of randomly selecting a man or someone who survived. Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223

13. Find the probability of randomly selecting a man or someone who survived. Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223

14. Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 = 0.929

15. Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Contingency Table Men Women Boys Girls Totals Survived 332 318 29 27 706 Died 1360 104 35 18 1517 Total 1692 422 64 45 2223 = 0.929 * NOT Mutually Exclusive *

16. P(A) and P(A) are mutually exclusive Complementary Events

17. P(A) and P(A) are mutually exclusive All simple events are either in A or A. Complementary Events

18. P(A) and P(A) are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1 Is there another form of writing this equation? Complementary Events