1. An oil company purchased an option on land in Alberta.

(a) Preliminary geologic studies assigned the following prior probabilities:

P(high-quality oil) = .50, P(medium-quality oil) = .20, and P(no oil) = .30.

What is the probability of finding oil?

(b) After 100 meters of drilling on the first well, a soil test was taken. A particular type

of soil was found. Previous experience indicates that the probabilities of finding this type

of soil are as follows: P(soil | high-quality oil) = .20, P(soil | medium-quality oil) = .80,

and P(soil | no oil) = .20 . What is the new probability of finding oil and the revised

probabilities for the types of oil?