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Addition Rules of Probability……

Addition Rules of Probability……. OBJECTIVE. Recognize Mutually Exclusive Events Use the Addition Rule of Probability. RELEVANCE. To find the likelihood of an event occurring by observing the long-term proportion in which a certain outcome is observed. Card Facts……. 52 cards in the deck

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Addition Rules of Probability……

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  1. Addition Rules of Probability……

  2. OBJECTIVE • Recognize Mutually Exclusive Events • Use the Addition Rule of Probability

  3. RELEVANCE To find the likelihood of an event occurring by observing the long-term proportion in which a certain outcome is observed.

  4. Card Facts…… • 52 cards in the deck • 4 suits • 13 cards in each suit (diamond, hearts, clubs, spades) • Face cards – jack, queen, king • 26 red cards; 26 black cards

  5. Mutually Exclusive Events…… • Events that cannot occur at the same time. • For example: Being a junior and being a senior are mutually exclusive.

  6. Getting a 4 and a 6 Getting an odd # and an even # Getting an odd# and a # less than 4 Getting a # greater than 4 and a # less than 4 Getting a 3 and an odd # Mutually Exclusive Mutually Exclusive Not M.E. Mutually Exclusive Not M.E. Determine which events are mutually exclusive when a single die is rolled…..

  7. Getting a 7 and J Getting a club and king Getting a face card and an ace Getting a face card and a spade M.E Not M.E. M.E. Not M.E. You Try…Which are mutually exclusive when a single card is drawn from a deck?......

  8. Addition Rule – M.E. Events…… • When 2 events are mutually exclusive, the probability that A or B will occur is

  9. Example…… • A box contains 3 glazed, 4 jelly, and 5 chocolate doughnuts. If a person selects one doughnut at random, find the probability that it is either glazed or chocolate.

  10. Answer…… • Sample Space = 3+4+5 = 12 doughnuts • P(glazed or choc) = P(glazed) + P(chocolate)

  11. Example…… • At a political rally, there are 20 republicans, 13 democrats, and 6 independents. If a person is selected at random, find the probability that he or she is either a democrat or an independent.

  12. Answer…… • Sample Space = 20+13+6=39 • P(dem orind) = P(dem)+P(ind)

  13. Example…… • A day of the week is selected at random. Find the probability that it is a day of the weekend.

  14. Answer…… • Sample Space = 7 days in a week P(Sat or Sun)= P(Sat) + P(Sun)

  15. Addition Rule – NOT Mutually Exclusive…… • When 2 events are NOT mutually exclusive, the probability that A or B will occur is • The Formal Addition Rule

  16. Example…… • A single card is drawn from a deck. Find the probability that it is a king or club.

  17. Example…… • In a hospital unit there are 8 nurses and 5 doctors. 7 nurses and 3 doctors are female. If a staff person is selected, find the probability that the subject is a nurse or a male. • Suggestion: Make a contingency table.

  18. Find the P(nurse or male) • Let n = nurse and m = male • P(n or m) = P(nurse) + P(m) – P(nurse and male)

  19. Example…… • On New Year’s Eve, the probability of a person driving while intoxicated is 0.32, the prob. of a person having an accident is .09, and the prob. of a person having an accident while intoxicated is .06. What is the probability of a person driving while intoxicated or having an accident?

  20. Answer…… • P(intox or acc) = P(intox) + P(acc) – P(intox and acc)

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