You have mineral rights on a piece of land that you believe may have oil undergr

Question

You have mineral rights on a piece of land that you believe may have oil underground. There is only a 15% chance that you will strike oil if you drill. Before you drill oil underground, you want to consult a geologist who can assess the promise of the piece of land. The geologist can tell you whether your prospects are “good” or “poor.” But she is not a perfect predictor. If there is oil, the conditional probability is 0.90 that she will say prospects are good. If there is no oil, the conditional probability is 0.80 that she will say poor.

Calculate the appropriate conditional probabilities that the geologist will predict you will strike oil and no oil.

Explanation / Answer

Ans:

Given that

P(oil)=0.15

P(not oil)=1-0.15=0.85

P(good/oil)=0.9

P(poor/oil)=1-0.9=0.1

P(poor/no oil)=0.8

P(good/no oil)=1-0.8=0.2

Now,find:

P(good)=P(good/oil)*P(oil)+P(good/no oil)*P(no oil)

=0.9*0.15+0.2*0.85=0.305

P(poor)=1-0.305=0.695

P(oil/good)=P(good/oil)*P(oil)/P(good)=0.9*0.15/0.305=0.4426

P(no oil/good)=P(good/no oil)*P(no oil)/P(good)=0.2*0.8/0.305=0.5574

P(oil/poor)=P(poor/oil)*P(oil)/P(poor)=0.1*0.15/0.695=0.0216

P(no oil/poor)=P(poor/no oil)*P(no oil)/P(poor)=0.8*0.85/0.695=0.9784

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