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)=0.4

P (no oil)= 0.3

a. What is the probability of finding oil (to 1 decimal)?

b. After 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 are given below.

P(Soil /High- quality oil) = 0.4

P(Soil/medium - quality oil)=0.4

P (Soil/no oil)= 0.2

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

P(Soil /High- quality oil) = ?

P(Soil/medium - quality oil)= ?

P (Soil/no oil)= ?

c. What is the new probability of finding oil (to 4 decimals)?