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1/2, 1/6, 1/6, 1/6 1)If you spin once, what is the probability of getting each dollar amount (fractions)? 2) If you spin twice, what is the probability of getting $100 and then $200? 3) If you spin twice, what is the probability of getting a sum of $600? 1/12 $100 $200 $300 $400 60° 90° 1/12

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6.5 Expected Value A collection of outcomes is partitioned into n events, no two of which have any outcomes in common. The probabilities of the n events occurring are p 1, p 2, p 3,..., p n where p 1 + p 2 + p 3 + p n = 1. The values of the n events are x 1, x 2, x 3,..., x n. E = p 1 x 1 + p 2 x 2 + p 3 x p n x n

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Example 1 Find the expected value. EP(E) E = 1(.20) + 2(.30) + 3(.10) + 4(.40) = 2.7 If I do this experiment 10 times, what total value would you expect to get?

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Example 2 You take an exam that has 4 possible answers for each question. You gain 3 points for each correct answer, lose 1 point for each incorrect answer, and do not gain or lose points for blank answers. If you do not know the answer to a question is it to your advantage to guess the answer? E = (3)(1/4) + (-1)(3/4) = 0

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Example 3 At a raffle, 2500 tickets are sold at $5 each for 3 prizes of $1000, $500, and $100. You buy one ticket. What is the expected value of your gain? E = 995(1/2500) + 495(1/2500) + 95(1/2500) + (-5)(2497/2500) = -$4.36 Gain,x$995$495$95-$5 Prob, p 1/ / 2500

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