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  Notation P(A or B) = P (event A occurs or event B occurs or they both occur) Definition

3. 3 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

4. 4 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.

5. 5 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

6. 6 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

7. 7 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

8. 8 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 45 2223 Contingency Table

9. 9 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 45 2223 Contingency Table

10. 10 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 45 2223 Contingency Table

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. 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 42264 45 2223 Contingency Table * Mutually Exclusive *

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 someone who survived. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 42264 45 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 someone who survived. Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 45 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 someone who survived. P(man or survivor) = 1692 + 706 - 332 = 2066 2223 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 45 2223 Contingency Table = 0.929

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. P(man or survivor) = 1692 + 706 - 332 = 2066 2223 2223 2223 2223 Men Women Boys Girls Totals Survived 332 31829 27 706 Died 1360 10435 18 1517 Total 1692 422 64 45 2223 Contingency Table * NOT Mutually Exclusive * = 0.929

16. 16 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

17. 17 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

18. 18 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)

19. 19 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Examples 1)A restaurant has 3 pieces of apple pie, 5 pieces of cherry and 4 pieces of pumpkin pie in its dessert case. If a customer selects a piece of pie what is the probability that it is cherry or pumpkin? Events are mutually exclusive P(Cherry or Pumpkin) = P(Cherry) + P(Pumpkin) = 5/12 + 4/12 = 9/12 = 3/4.

20. 20 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Examples 1)A single card is selected from a standard deck of cards. What is the probability that it is a king or club? Events are not mutually exclusive P(King or Club) = P(King) + P(Club) – P(King and Club) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13.

21. 21 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Assignment Page 139: 1- 25 all