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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 3-3 Addition Rule. M ARIO F . T RIOLA. E IGHTH. E DITION. 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.

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M ARIO F . T RIOLA

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  1. STATISTICS ELEMENTARY Section 3-3 Addition Rule MARIO F. TRIOLA EIGHTH EDITION

  2. 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. 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

  4. 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. Compound Event

  5. 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. Compound Event

  6. Events A and B are mutually exclusive if they cannot occur simultaneously. Definition

  7. Events A and B are mutually exclusive if they cannot occur simultaneously. Definition Total Area = 1 P(A) P(B) P(A and B) Overlapping Events Figures 3-5

  8. Events A and B are mutually exclusive if they cannot occur simultaneously. Definition Total Area = 1 Total Area = 1 P(A) P(B) P(A) P(B) P(A and B) Overlapping Events Non-overlapping Events Figures 3-5 and 3-6

  9. 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)

  10. 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

  11. 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

  12. 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

  13. 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 *

  14. 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

  15. 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

  16. Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 2066 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

  17. Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = 1692 + 706 - 332 = 2066 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 *

  18. P(A) and P(A) are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1 Complementary Events

  19. Rules of Complementary Events P(A) + P(A) = 1 = 1 - P(A) P(A) = 1 - P(A) P(A)

  20. Figure 3-8 Venn Diagram for the Complement of Event A Total Area = 1 P (A) P (A) = 1 - P (A)

  21. Examples • 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.

  22. Examples • 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.

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