In Problem 36, the Blue Sox general manager has asked a superscout to assign a probability to each of the three states of nature for the pitchers during the next 10 years. The scout estimates there is a .10 probability that these pitchers at this stage of their careers will have no injuries, a .60 probability that they will have a career with the normal number of injuries, and a .30 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?

Jose Diaz ………… $ 97.3

Jerry Damon ……… $121.5

Frank Thompson ….. $ 73.5

Derek Rodriguez … $103.4

Ken Griffin ………. $ 85.7

c. Suppose that the general manager asked the superscout to determine the probabilities of each state of nature for each individual pitcher, and the results were as follows:

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.

Physical Condition Pitcher No injuries Normal Excessive Injuries 0.30 0.45 0.47 0.35 0.25 Jerry Damon Frank Thompson Derek Rodriguez Ken Griffin 0.13 0.40 0.45 0.50 0.15 0.20 0.40 0.10 0.60