Physicians have been approached by a market research firm that offers to perform a study for $5000. Their experience enables them to use Bayes' theorem to make the following statements of probability:

probability of a favorable market given a favorable study = 0.82
probability of an unfavorable market given a favorable study = 0.18
probability of a favorable market given an unfavorable study = 0.11
probability of an unfavorable market given a unfavorable study = 0.89
probability of a favorable research study = 0.55
probability of a favorable research study = 0.45

a) Develop a new decision tree to reflect the options now open to the market study (the previous decision tree had the following information: $100,000 profit for favorable market, $40,000 loss for unfavorable market, or do nothing with zero cost-- 50-50 chance of success.)
b) Use the EMV approach to recommend a strategy.
c) What's the expected value of sample information? How much might the physicians be willing to pay for a market study?