Question

3.22 ([1] 3.70) An oil prospector will drill a succession of holes in a given area to find productive well. The probability that he 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 ten wells, what is the probability that he will fail to find a productive well? c) The prospector drills holes until he finds a productive well. How many holes would the prospector expect to drill?

Answer 1

a) 0.128

b) 0.107

c) 5

Explanation:

P(successful on a given trial) = 0.2

P(unsuccessful on a given trial)=0.8

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

This is possible when being unsuccessful in the first and second trial, successful in the third trial. This probability equals

=P(unsuccessful on a given trial) × P(unsuccessful on a given trial) × P(successful on a given trial) = 0.8 × 0.8 × 0.2 = 0.128

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?

This probability equals
`0.8^(10)` ≈ 0.107

c) The prospector drills holes until he finds a productive well. How many holes would the prospector expect to drill?

This probability equals

`(1)/(P(successful on a given trial))` =
`(1)/(0.2)` = 5