Question: 32. In Problem S1-31 the Sharks general manager has asked a super scout to assign a probability to each of the three states of nature

32. In Problem S1-31 the Sharks general manager has asked a super scout to assign a probability to each of the three states of nature that may occur for the pitchers during the next 10 years. The scout estimates that there is a .08 probability that these pitchers at this stage of their careers will have no injuries, a .56 probability that they will have a career with the normal amount of injuries, and a .36 probability that they will have excessive injuries. (a) Using expected value, determine the best pitcher to sign. (b) Given the following 10-year contract price for each pitcher (in $ millions), which would you recommend signing? Miguel Garcia $96.2 Juan Ramon $118.4 Fred Terry $81.6 Alan Rodriguez $102.8 Jared Washburn $75.7 (c) Suppose that the general manager asked the super scout to determine the probabilities of each state of nature for each individual pitcher, as follows: PHYSICAL CONDITION PITCHER NO INJURIES NORMAL EXCESSIVE INJURIES Miguel Garcia .27 .46 .27 Juan Ramon .14 .45 .41 Fred Terry .37 .35 .28 Alan Rodriguez .43 .45 .12 Jared Washburn .21 .57 .22 Determine the expected number of wins for each pitcher and combined with the contract price in part (b), indicate which pitcher you would recommend signing.

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