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?