Chapter 5, Problem 13P

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

$\begin{array}{c}P\left(\text{high-quality oil}\right)=0.50\\ P\left(\text{medium-quality oil}\right)=0.20\\ P\left(\text{no oil}\right)=0.30\end{array}$

1. a. What is the probability of finding oil?
2. 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 are as follows.

$\begin{array}{c}P\left(\text{soil }|\text{ high-quality}\text{ oil}\right)=0.20\\ P\left(\text{soil | medium-quality oil}\right)=0.80\\ P\left(\text{soil | no oil}\right)=0.20\end{array}$

How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?