1. 1 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 3-3 Addition Rule

2. 2 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman  Compound Event Any event combining 2 or more simple events Definition

3. 3 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman  Compound Event Any event combining 2 or more simple events  Notation P(A or B) = P (event A occurs or event B occurs or they both occur) Definition

4. 4 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman General Rule When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. Compound Event

5. 5 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 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 B both occur at the same time. Compound Event

6. 6 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman 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 B both 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 is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes. Compound Event

7. 7 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously.

8. 8 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 Total Area = 1 P(A) P(B) P(A and B) Overlapping Events

9. 9 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 and 3-6 Total Area = 1 P(A) P(B) P(A and B) Non-overlapping Events Overlapping Events

10. 10 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Figure 3-7 Applying the Addition Rule P(A or B) Addition Rule Are A and B mutually exclusive ? P(A or B) = P(A)+ P(B) - P(A and B) P(A or B) = P(A) + P(B) Yes No

11. 11 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table

12. 12 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table

13. 13 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or a boy. P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table

14. 14 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or a boy. P(man or boy) = 1692 + 64 = 1756 = 0.790 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table * Mutually Exclusive *

15. 15 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table

16. 16 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table

17. 17 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table = 0.929

18. 18 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 56 2223 Contingency Table * NOT Mutually Exclusive * = 0.929

19. 19 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive

20. 20 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A.

21. 21 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1

22. 22 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Rules of Complementary Events P(A) + P(A) = 1

23. 23 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman P(A) Rules of Complementary Events P(A) + P(A) = 1 = 1 - P(A)

24. 24 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman P(A) + P(A) = 1 = 1 - P(A) P(A) = 1 - P(A) P(A) Rules of Complementary Events

25. 25 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Figure 3-8 Venn Diagram for the Complement of Event A Total Area = 1 P (A) P (A) = 1 - P (A)