An oil company purchased an option on Land in Alaska. Preliminary geologic studies assigned the following prior probabilities:
P(high-quality oil) = .3
P(medium-quality oil)=.3
P(no oil)=.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) = .2
P(soil | medium-quality oil) = .7
P(soil | no oil)=.3
What is the new probability of finding oil?