Question

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

P(high-quality oil) = 0.3
P(medium-quality oil)= 0.3
P(no oil)= 0.4

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) = 0.2
P(soil | medium-quality oil) = 0.7
P(soil | no oil)= 0.3

What is the new probability of finding oil?