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

Answer 1

0.128 is the probability that the third hole drilled is the first to yield a productive well.

Explanation:

We are given the following information in the question:

The probability that he is successful on a given trial is 0.2

p = 0.2

q = 1 - p = 0.8

We define the geometric probability as:

`P(X=x) = p(1-q)^(x-1)`

For this we have x = 3, putting the values we have:

`P(X=x) = p(1-q)^(x-1)\\P(x=3) = 0.2(0.8)^2 = 0.128 = 12.8\%`

0.128 is the probability that the third hole drilled is the first to yield a productive well.