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 1

a) The probability that the third hole drilled is the first to yield a productive well is given by the following sequence of events: the first two holes must be unproductive, followed by a productive third hole. The probability of each of these events happening is:

- Probability of an unproductive hole: 0.8

- Probability of two unproductive holes in a row: 0.8