Unit 3-3

Unit 3-3 - Probability Denoted by P(Event) favorable...

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Probability Denoted by P(Event) outcomes total outcomes favorable ) ( = E P This method for calculating probabilities is only appropriate when the outcomes of the sample space are equally likely.
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Experimental Probability The relative frequency at which a chance experiment occurs Flip a fair coin 30 times & get 17 heads 30 17
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Law of Large Numbers As the number of repetitions of a chance experiment increase, the difference between the relative frequency of occurrence for an event and the true probability approaches zero.
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Basic Rules of Probability Rule 1. Legitimate Values For any event E, 0 < P(E) < 1 Rule 2. Sample space If S is the sample space, P(S) = 1
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Rule 3. Complement For any event E, P(E) + P(not E) = 1
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Rule 4. Addition If two events E & F are disjoint, P(E or F) = P(E) + P(F) (General) If two events E & F are not disjoint, P(E or F) = P(E) + P(F) – P(E & F)
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Ex 1) A large auto center sells cars made by many different manufacturers. Three of these are Honda, Nissan, and Toyota. (Note: these are not simple events since there are many types of each brand.) Suppose that P(H) = . 25, P(N) = .18, P(T) = .14. Are these disjoint events? P(H or N or T) = P(not (H or N or T) = yes .25 + .18+ .14 = .57 1 - .57 = .43
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Ex. 2) Musical styles other than rock and pop are becoming more popular. A survey of college students finds that the probability they like country music is . 40. The probability that they liked jazz
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Unit 3-3 - Probability Denoted by P(Event) favorable...

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