A nuclear power company is deciding whether to build a nuclear plant at Chico Canyon or at Pleasantville. The cost of building the power plant is 14 million at Chico and 20 million at Pleasantville. If the company builds at Chico, however, and an earthquake occurs at Chico during the next 5 years, construction will be terminated and the company will lose 14 million (and will still have to build a power plant at Pleasantville). Without further information, the company believes there is a 20 chance that an earthquake will occur at Chico during the next 5 years.
(A) Construct a decision tree to help the power company decide what to do. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) Where should the power company build the plant? What is the expected cost?
(C) Suppose that a geologist (and his team) can be hired to analyze the fault structure at Chico Canyon. He will either predict whether an earthquake will occur or not. If the geologist is perfectly reliable, what is the most the company should be willing to pay for his services?
(D) Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologists past record indicates that he will predict an earthquake on 90 of the occasions for which an earthquake will occur and no earthquake on 85 of the occasions for which an earthquake will not occur. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions?
(E) Should the company hire the geologist if his fee is 1.5M?
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