A nuclear power company is deciding whether to build a nuclear plant at Chico Ca

Question

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. Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist’s 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 is the maximum amount the company can pay the geologist?

Explanation / Answer

Chico canyon -

Cost - $14 million

Probability of earthquake - 0.2, probability of no earthquake - 0.8

In case there is earthquake,

Geologist prediction correct - 0.9, Geologist's prediction incorrect - 0.1

In case there is no earthquake,

Geologist's prediction correct - 0.85, Geologist's prediction incorrect - 0.15

The chances of correct prediction by the geologist are - 0.2*0.9 + 0.8*0.85 = 0.18 + 0.68 = 0.86 or 86%

Therefore, the maximum amount that the company can pay is 86% of his usual fees.

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