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[Solved] An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil)=0.50

Question: An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.

\(P(\) high-quality oil \()=0.50\) \(P(\) medium-quality oil \()=0.20\)

\[P(\text { no oil }) \quad=0.30\]
  1. What is the probability of finding oil?
  2. After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are
\[\begin{array}{ll} P(\text { soil } \mid \text { high-quality oil }) & =0.20 \\ P(\text { soil } \mid \text { medium-quality oil }) & =0.80 \\ P(\text { soil } \mid \text { no oil }) & =0.20 \end{array}\]

How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

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