An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. PP( text{high-quality oil})=.50 P(text{medium-quality oil} )=.20 P( text{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( text{soil | high-quality oil} )=.20 P( text{soil | medium-quality oil})=.80 P( text{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?

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. PP( text{high-quality oil})=.50 P(text{medium-quality oil} )=.20 P( text{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( text{soil | high-quality oil} )=.20 P( text{soil | medium-quality oil})=.80 P( text{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?

Question
Polynomial arithmetic
asked 2020-12-29
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
\(PP( \text{high-quality oil})=.50 P(\text{medium-quality oil} )=.20 P( \text{no oil} )=.30\)
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.
\(P( \text{soil | high-quality oil} )=.20 P( \text{soil | medium-quality oil})=.80 P( \text{soil | no oil})=.20\)
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

Answers (1)

2020-12-30
Given:
\(P( \text{no oil}) = 0.30\)
a. Complement rule:
\(P( \text{not} A ) = 1 - P(A)\)
Use the complement rule:
\(P(\text{oil}) = 1 - P(\text{no oil}) = 1 - 0.30 = 0.70\)
b. We are most likely to find the type of soil, when we have found medium-quality oil.
The probabilities remain unchanged> becase the given probability only effect the probability of finding soil and not the probability of finding oil.
0

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