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Addition Rules of Probability……
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OBJECTIVE Recognize Mutually Exclusive Events
Use the Addition Rule of Probability
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RELEVANCE To find the likelihood of an event occurring by observing the long-term proportion in which a certain outcome is observed.
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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
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Mutually Exclusive Events……
Events that cannot occur at the same time. For example: Being a junior and being a senior are mutually exclusive.
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Determine which events are mutually exclusive when a single die is rolled…..
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 Not M.E.
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You Try…Which are mutually exclusive when a single card is drawn from a deck?......
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.
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Addition Rule – M.E. Events……
When 2 events are mutually exclusive, the probability that A or B will occur is
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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.
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Answer…… Sample Space = 3+4+5 = 12 doughnuts
P(glazed or choc) = P(glazed) + P(chocolate)
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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.
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Answer…… Sample Space = =39 P(dem or ind) = P(dem)+P(ind)
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Example…… A day of the week is selected at random. Find the probability that it is a day of the weekend.
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Answer…… Sample Space = 7 days in a week
P(Sat or Sun)= P(Sat) + P(Sun)
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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
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Example…… A single card is drawn from a deck. Find the probability that it is a king or club.
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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.
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Find the P(nurse or male)
Females Males Total Nurse 7 1 8 Doctors 3 2 5 10 13 Let n = nurse and m = male P(n or m) = P(nurse) + P(m) – P(nurse and male)
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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 What is the probability of a person driving while intoxicated or having an accident?
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Answer…… P(intox or acc) = P(intox) + P(acc) – P(intox and acc)
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