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) $p=0.8^2*0.2=0.128.$

(b) $p=0.8^{10}=0.1074.$