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A power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo and $20 million at Roy Rogers City. If the company builds at Diablo and an earthquake occurs at Diablo during the next five years, construction will be terminated and the company will lose $10 million (and will still have to build a power plant at Roy Rogers City). At this point the company believes there is a 20% chance that an earthquake will occur, at Diablo during the next five years. a. Draw a decision tree for this situation. Show all probabilities, costs, and expected values at appropriate places on the tree. (5 pts) b. Recommend a decision to the power company. What is the expected cost of this decision? (2 pts) c. What is the expected value of perfect information (EVPI) regarding the possibility of an earthquake at Diablo Canyon? (5 pts) For $1 million, a geologist can be hired to analyze the fault structure at Diablo Canyon. She will predict either that an earthquake will occur or that an earthquake will not occur. The geologist's past record indicates that she predicted an earthquake 95% of the times that an earthquake did occur, and she predicted no earthquake 90% of the times that an earthquake did not occur d. Construct a joint-probability table for this situation. (8 pts) a se e. Suppose this geologist is hired. What is the probability that she will predict that an earthquake will occur? (2 pt) el materie van de mensen in het team van de entrenat f. Suppose this geologist is hired and predicts that an earthquake will occur. What is the probability that there will be an earthquake at Diablo Canyon? (3 pts) 8. Suppose this geologist is hired and predicts that an earthquake will not occur. What is the probability there will be an earthquake at Diablo Canyon? (3 pts) h. Modify the tree in (a) to include the new alternative (hiring the geologist). Show all probabilities, costs, and expected values at appropriate places on the tree. (6 pts) i. Should the power company hire this geologist? If yes, what is the expected cost of this decision? (3 pts) j. What is the most this company should be willing to pay this geologist for her predictions? (3 pts) A power company is deciding whether to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo and $20 million at Roy Rogers City. If the company builds at Diablo and an earthquake occurs at Diablo during the next five years, construction will be terminated and the company will lose $10 million (and will still have to build a power plant at Roy Rogers City). At this point the company believes there is a 20% chance that an earthquake will occur, at Diablo during the next five years. a. Draw a decision tree for this situation. Show all probabilities, costs, and expected values at appropriate places on the tree. (5 pts) b. Recommend a decision to the power company. What is the expected cost of this decision? (2 pts) c. What is the expected value of perfect information (EVPI) regarding the possibility of an earthquake at Diablo Canyon? (5 pts) For $1 million, a geologist can be hired to analyze the fault structure at Diablo Canyon. She will predict either that an earthquake will occur or that an earthquake will not occur. The geologist's past record indicates that she predicted an earthquake 95% of the times that an earthquake did occur, and she predicted no earthquake 90% of the times that an earthquake did not occur d. Construct a joint-probability table for this situation. (8 pts) a se e. Suppose this geologist is hired. What is the probability that she will predict that an earthquake will occur? (2 pt) el materie van de mensen in het team van de entrenat f. Suppose this geologist is hired and predicts that an earthquake will occur. What is the probability that there will be an earthquake at Diablo Canyon? (3 pts) 8. Suppose this geologist is hired and predicts that an earthquake will not occur. What is the probability there will be an earthquake at Diablo Canyon? (3 pts) h. Modify the tree in (a) to include the new alternative (hiring the geologist). Show all probabilities, costs, and expected values at appropriate places on the tree. (6 pts) i. Should the power company hire this geologist? If yes, what is the expected cost of this decision? (3 pts) j. What is the most this company should be willing to pay this geologist for her predictions? (3 pts)
