An oil prospector will drill a succession of holes in a give

An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that the prospector is successful on a given trial is 0.2

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 10 wells, what is the probability that prospector will fail to find a productive well?

Solution

a)The probability that the third hole drilled is the first to yield a productive well is: 0.80*0.8*0.2=0.128

b)The probability that he will fail to find a productive well in 10 drills is: 0.8^10=0.107