2. A nuclear power company is trying to decide whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $15 million at Diablo and $20 million at Roy Rogers City. Diablo is known to be in earthquake zone. If the company decides to build at Diablo and an earthquake happens in Diablo in the next 5 years, the company will lose the $15 million worth plant (and, due to agreements with the state officials, it will still have to build a power plant at Roy Rogers City). Historical records show that there is about 10% chance that an earthquake will hit Diablo during the next 5 years. At a cost of C dollars, a geologist can be hired to analyze the fault structure at Diablo Canyon. The geologist will predict either that an earthquake will hit or that it will not hit. The geologists past record indicates that she correctly predicts an earthquake only 80% of the occasions, and correctly predicts no earthquake 95% of the occasions.

a. [2 points] What is the probability that the geologist will predict that an earthquake will hit Diablo in the next 5 years? Answer to three decimal places.

b. [2 points] What is the probability that the geologist may have raised a false earthquake alarm? Answer to three decimal places.

c. [2 points] What is the probability that the geologist may have falsely concluded a safe (i.e., no earthquake) zone? Answer to three decimal places.

d. [8 points] Assume C = $100,000. Using your answers from parts (a)-(c), construct a decision tree model to layout the sequence of decisions and chance events in this decision problem. Note all the immediate payoffs/costs for each branch as well as the probabilities for all chance branches.

e. [3 points] Implementation. Implement your model from part (d) in Excel. Identify the best strategy that minimizes the expected cost. Clearly write out the optimal strategy and the minimum expected cost associated with this strategy? Minimum expected cost: Optimal strategy:

f. [4 points] What is the maximum value of C that this company should be willing to pay the geologist? g. [4 points] Compute expected value of perfect information regarding the earthquake.