In Problem 14, the management of the Oakland Bombers is considering hiring superscout Jerry McGuire to evaluate the team’s chances for the coming season. McGuire will evaluate the team, assuming that it will sign one of the four free agents. The team’s management has determined the probability that the team will have a losing record with any of the free agents to be .21 by averaging the probabilities of losing for the four free agents in Problem 33. The probability that the team will have a competitive season but not make the playoffs is developed similarly, and it is .35. The probability that the team will make the playoffs is .44. The probability that McGuire will correctly predict that the team will have a losing season is .75, whereas the probability that he will predict a competitive season, given that it has a losing season, is .15, and the probability that he will incorrectly predict a playoff season, given that the team has a losing season, is .10.
The probability that he will successfully predict a competitive season is .80, whereas the probability that he will incorrectly predict a losing season, given that the team is competitive, is .10, and the probability that he will incorrectly predict a playoff season, given the team has a competitive season, is .10. The probability that he will correctly predict a playoff season is .85, whereas the probability that he will incorrectly predict a losing season, given that the team makes the playoffs, is .05, and the probability that he will predict a competitive season, given the team makes the playoffs, is .10. Using decision tree analysis and posterior probabilities, determine the decision strategy the team should follow, the expected value of the strategy, and the maximum amount the team should pay for Jerry McGuire’s predictions.