Question: Lord Thomas Bayes owns a crumbling castle in England. The revenue from visitors to the property is no longer enough to cover the operating costs and he must decide whether to Itliegawerty or build a theme park on the grounds to draw more visitors. The historical heritage society has offered to buy the property for $8 million_ If he builds a theme park, he estimates there is a 60% chance it will succeed and produce a profit of $25 million. Otherwise it will fail and he will incur a loss of $5 million. He could start building any time but a contact at the tourist authority suggested that he should first hire Seyab Yaz, an expert on leisure developments, to assess the prospects for the venture. Mr. Yaz has a good record — accurately predicting the success of similar ventures 70% of the time and accurately predicting the failure of such ventures 80% of the time. (20 points)

1. Estimate the probabilities of success or failure conditional on the prediction of Mr. Seyab Yaz.
2. Draw the decision tree with labels for decision nodes and chance nodes_ Put payoffs at the end points, probabilities at the chance nodes, and calculate expected values working backward based on the optimal decisions at each point.
3. Is there any value to obtaining Mr. Yaz's prediction? Is so, what is that value?

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