An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil) = .50
P(medium-quality oil) = .20
P(no oil) = .30
a. What is the probability of finding oil?
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test follow.
P(soil | high-quality oil) = .20
P(soil | medium-quality oil) = .80
P(soil | no oil) = .20
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?