Question

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

P(high-quality oil) = 0.40 

P(medium-quality oil) = 0.15 

P(no oil) = 0.45

 a. What is the probability of finding oil (to 2 decimals)?

 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 given below.

 P(soil high-quality oil) = 0.20

 P(soil medium-quality oil) = 0.85

 P(soil no oil) = 0.20

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

P(high-quality oil soil) 

P(medium-quality oilsoil) 

P(no oil soil)

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

According to the revised probabilities, what is the quality of oil that is most likely to be found? 

• High-quality 

• Medium-quality 

• No oil

Answer 1

Part (A)

P(no oil) = 0.45

=> P (oil) = 1 - P(no oil)

=> P (oil) = 1 - 0.45

=> P (oil) = 0.55

Probability of finding the oil is 0.55

Answer: 0.55

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Part (B)

Let's assume; High quality oil = Ai

Medium quality oil = A2

No oil = A3

P(AI) P(soil 1 Ai) 0.4 0.2 P (Ail Soil) 0.2689 Event High Quality oil (A1) Medium Quality oil (A2) No oil (A3) 0.15 0.85 P (Ain Soil) 0.08 0.1275 0.09 P (Soil) = 0.2975 0.4286 0.3025 0.45 0.2

P (Ai ∩ S) = P (Ai) * P (S I Ai)

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P(S) = P(A1 ∩ S) + P (A2 ∩ S) + P (A3 ∩S)

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P (Ai I S) = P (Ai ∩ S) / P(S)

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Answer:

P ( high quality oil I soil) = P (A1 I S)

=> P ( high quality oil I soil) = 0.2689

--

P ( medium quality oil I soil) = P (A2 I S)

=> P ( medium quality oil I soil) = 0.4286

--

P ( no oil I soil) = P (A3 I S)

=> P ( no oil I soil) = 0.3025

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New probability of finding oil.

i.e., P (oil I soil) = 1 - P(no oil I soil)

=> P (oil I soil) = 1 - 0.3025

=> P (oil I soil) = 0.6975

Answer: 0.6975

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Part (c)

P ( high quality oil I soil) = 0.2689

P ( medium quality oil I soil) = 0.4286

P ( no oil I soil) = 0.3025

According to revised probabilities, medium quality oil is most likely to be found.

Answer: Medium quality.