The Wisteria University athletic department is considering a campaign next year to raise funds for a new athletic field. To a large extent, the response to the campaign depends on how successful the soccer team is in the fall. In the past they have had winning seasons 60% of the time. If they have a winning season (G), many alumni will contribute and the campaign will raise $3 million. If they have a losing season (P), very few will contribute and they will lose $2 million. If the campaign does not take place, no cost is incurred. On September 1, prior to the start of the season, the athletics department must decide whether to conduct the campaign next year. d) A famous soccer guru, William Walsh, has offered to evaluate whether the team will have a winning season. For $100,000 he will evaluate the team's spring and preseason practices. William will give his prediction on September 1 as to what type of season, G or P, the team will have. In similar situations in the past, when evaluating teams with winning seasons 50% of the time, his predictions were true 75% of the time. If this team is considered to have a longer winning tradition, if William predicts a winning season, what is the a posteriori probability that it will actually be so? What is the a posteriori probability that it will be a losing one? If William predicts a losing season, what is the a posteriori probability that it will be a winning one? And that it will be a losing one? Show how to obtain the answers in a probability tree. e) Draw the decision tree for the complete problem by hand. Analyze it to determine the optimal policy, i.e., whether to hire William and whether to run the campaign.
The Wisteria University athletic department is considering a campaign next year to raise funds for a new athletic field. To a large extent, the response to the campaign depends on how successful the soccer team is in the fall. In the past they have had winning seasons 60% of the time. If they have a winning season (G), many alumni will contribute and the campaign will raise $3 million. If they have a losing season (P), very few will contribute and they will lose $2 million. If the campaign does not take place, no cost is incurred. On September 1, prior to the start of the season, the athletics department must decide whether to conduct the campaign next year.
d) A famous soccer guru, William Walsh, has offered to evaluate whether the team will have a winning season. For $100,000 he will evaluate the team's spring and preseason practices. William will give his prediction on September 1 as to what type of season, G or P, the team will have. In similar situations in the past, when evaluating teams with winning seasons 50% of the time, his predictions were true 75% of the time. If this team is considered to have a longer winning tradition, if William predicts a winning season, what is the a posteriori probability that it will actually be so? What is the a posteriori probability that it will be a losing one? If William predicts a losing season, what is the a posteriori probability that it will be a winning one? And that it will be a losing one? Show how to obtain the answers in a probability tree.
e) Draw the decision tree for the complete problem by hand. Analyze it to determine the optimal policy, i.e., whether to hire William and whether to run the campaign.
Note:
please, bartleby expert, make sure that the images you upload can be seen, because the last time you answered me, they could not be seen.
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The prior probability of winning season (G) = 0.60
Prior probability of a losing season = 1 - 0.60 = 0.40
The expected payoff of winning = $3 million
The expected payoff of losing = - $2 million
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