An oil prospector will drill a succession of holes in a

Chapter 3, Problem 70E

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QUESTION:

An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.

a What is the probability that the third hole drilled is the first to yield a productive well?

b If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

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QUESTION:

An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.

a What is the probability that the third hole drilled is the first to yield a productive well?

b If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

ANSWER:

Step 1 of  2

a) We have to find the probability that the third hole drilled is the first to give productive well

The probability of successful well is p = 0.2

Then q = 1 - p

            = 1 - 0.2

            = 0.8

The pmf of geometric distribution is \(P(X)=q^{x-1} p\)

Now

\(\begin{aligned}
P(3) & =(0.8)^{3-1}(0.2) \\
& =0.128
\end{aligned}\)

Hence the probability that the third hole drilled is the first to give productive well is 0.128

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