Problem 70E

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?

Solution

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

Now

=0.128

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