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.

Transcribed Image Text:

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