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first year probability question for geniuses?

Suppose that the subjective probabilities for

nding oil are p(oil)=0.5 and p(no oil)=0.5. Your

company drills for 500ft and

nds no oil, but they sample the soil at 500ft. From experience

the company knows that the conditional probability of

nding this type of soil given that oil

is present is 0.2, while the probability of

nding this type of soil given that no oil is present

is 0.8. What is the posterior probability of

nding oil?

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