"What is the most Stuart should pay for clairvoyance on uncertainty B before making decision A? Assume you cannot really access Clairvoyance, but you have a detector you can use to gather information about Distinction B before making Decision A. Let us refer to the top branch of Distinction B as Possibility X and the bottom branch of Distinction B as Possibility Y. When Possibility X materializes, the detector correctly predicts it in 60% of the cases and predicts Possibility Y in 40% of the cases. When Possibility Y materializes, the detector correctly predicts it in 90% of the cases and predicts Possibility X in 10% of the cases. Model the decision to purchase the detector and determine its value for just this decision."

Question to be answered: Consider the activity above, assume you have a second detector you can use to gather information about Distinction B before making Decision A. When Possibility X materializes, the detector correctly predicts it in 60% of the cases and predicts Possibility Y in 40% of the cases. When Possibility Y materializes, the detector correctly predicts it in 90% of the cases and predicts Possibility X in 10% of the cases. Model the decision to purchase both detectors and determine their value for just this decision.

For Problems 6,7 , and 8 , consider the decision situation given in the following decision tree where the dollar values are winnings and the probabilities are the assessments of the deal's owner. Suppose Stuart, who is risk-neutral, owned the deal below