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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. Definition. Compound Event Any event combining 2 or more simple    events Notation

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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 Definition

  3. 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. 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. 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

  6. 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

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

  8. 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

  9. 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

  10. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student with a birthday in May

  11. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student with a birthday in May • The events ARE mutually exclusive.

  12. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student who was born on a Monday.

  13. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a student with a birthday in March • Selecting a student who was born on a Monday. • The events are NOT mutually exclusive.

  14. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a full-time UCLA student • Selecting a full-time University of Notre Dame student

  15. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a full-time UCLA student • Selecting a full-time University of Notre Dame student • The events ARE mutually exclusive.

  16. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a senior in high school. • Selecting a student with a part-time job.

  17. Example: Mutually Exclusive • Determine whether the events are mutually exclusive. • Selecting a senior in high school. • Selecting a student with a part-time job. • The events are NOT mutually exclusive.

  18. 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)

  19. 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 56 2223

  20. 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 56 2223

  21. 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 56 2223

  22. 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 56 2223 * Mutually Exclusive *

  23. 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 56 2223

  24. 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 56 2223

  25. 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 56 2223 = 0.929

  26. 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 56 2223 = 0.929 * NOT Mutually Exclusive *

  27. Complementary Events

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

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

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

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

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

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

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

  35. Example: Complementary Events • If a person is randomly selected, find the probability that his or her birthday is not in October. Ignore the leap years.

  36. Example: Complementary Events • If a person is randomly selected, find the probability that his or her birthday is not in October. Ignore the leap years. • P(Birthday not in October)

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