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Question: There is a throwing accuracy game in which a velcro board is hung on the wall (see Figure) and players throw small prickly balls that stick on the board. Points are awarded to players depending on the region in which each prickly ball lands. The probability that a prickly ball lands in any particular one of the outer grey regions is , the probability that a prickly ball landsin any particular one of the white regions is , and the probability that a prickly ball lands in the center oval is .
(a) What assumption has been made in assigning these probabilities?
(b) What is the probability of hitting the upper-left-most region, given that you hit a region that is not white?
(c) You are awarded one point if your prickly ball lands on an outer grey region, three points if your prickly ball lands in a white region, and five points if your prickly ball lands within the oval. What is your expected number of points?
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