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Unformatted text preview: Homework # 2 Solutions The George Washington University ApSc 116 1 / 8 Problem (Page 55 # 9) Suppose that a box contains one blue card and four red cards, which are labeled A, B, C, and D. Suppose also that two of these five cards are selected at random, without replacement. a. If it is known that card A has been selected, what is the probability that both cards are red? b. If it is known that at least one red card has been selected, what is the probability that both cards are red? Solution: a. If card A has been selected each of the other four cards is equally likely to be the other selected card. Since three of these four cards are red, the required probability is 3 / 4. b. We know, without being told, that at least one red card must be selected, so this information does not affect the probability of any events. We have Pr (both cards red) = Pr ( R 1 ) Pr ( R 2  R 1 ) = 4 5 · 3 4 = 3 5 . 2 / 8 Problem (Page 65 # 18) Determine the probability that boy A will hit the target before B does. Solution: Let E denote the probability that boy A hits the target before boy B. There can be two methods of solving this problem. The first method is to note that the event E can occur in two different ways: (i) If A hits the target on the first throw, which happens with probability 1 3 ....
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 Fall '08
 TomMazzuchi
 Conditional Probability, Probability, 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 j, 1 3 4 j

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