An oil company purchased an option on land in Alaska. Preliminary geologic studi
ID: 3074301 • Letter: A
Question
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. P(high-quality oil) = 0.60 P(medium-quality oil) = 0.20 P(no oil) = 0.20 If required, round your answers to two decimal places. (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 are as follows. P(soil | high-quality oil) = 0.20 P(soil | medium-quality oil) = 0.80 P(soil | no oil) = 0.20 How should the firm interpret the soil test? The probability of finding oil is good. Given the probability of finding good soil, the oil company is more likely to find which oil? What are the revised probabilities? What is the new probability of finding oil?
Explanation / Answer
Answer:
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)
=
0.50
P(medium-quality oil)
=
0.20
P(no oil)
=
0.30
If required, round your answers to two decimal places.
(a)
What is the probability of finding oil? 0.70
(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.
P(soil | high-quality oil)
=
0.20
P(soil | medium-quality oil)
=
0.80
P(soil | no oil)
=
0.20
How should the firm interpret the soil test? What are the revised probabilities?
Events
P(Ai)
P(S | Ai)
P(Ai ? S)
P(Ai | S)
High Quality (A1)
0.5
0.2
0.1
0.3125
Medium Quality (A2)
0.2
0.8
0.16
0.5
No Oil (A3)
0.3
0.2
0.06
0.1875
P(S)=
0.32
What is the new probability of finding oil? 0.3125+0.5 =0.8125
P(high-quality oil)
=
0.50
P(medium-quality oil)
=
0.20
P(no oil)
=
0.30