   # An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P (high-quality oil) = .50 P (medium-quality oil) = .20 P (no oil) = .30 a. What is the probability of finding oil? 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 follow. P (soil | high-quality oil) = .20 P (soil | medium-quality oil) = .80 P (soil | no oil) = .20 How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4, Problem 59SE
Textbook Problem
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## An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.    P(high-quality oil) = .50    P(medium-quality oil) = .20    P(no oil) = .30 a. What is the probability of finding oil? 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 follow.     P(soil | high-quality oil) = .20    P(soil | medium-quality oil) = .80    P(soil | no oil) = .20How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

a.

To determine

Compute the probability of finding oil.

### Explanation of Solution

Calculation:

The given prior probabilities are as follows:

P(high-quality oil)=0.50P(medium-quality oil)=0.20P(no oil)=0.30

Addition Law for mutually exclusive events:

For mutually exclusive events, the addition law states that P(AB)=P(A)+P(B)

b.

To determine

Explain how the firm should interpret the results. Compute the revised probabilities and new probability of finding oil.

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