Question

An article on polygraph testing of FBI agents indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is 0.15. Let x be the number of trustworthy FBI agents tested until someone fails the test. What is the probability that the first false-positive will occur when the third person is tested

Answer 1

`Probability = 0.108375`

Explanation:

Given

Let the probability of false positive be represented with p

`p = 0.15`

Required

Determine the probability the first occurrence of p was at the third person

We have that:

`p = 0.15`

The probability that a trustworthy person do not fail the test (q) is:

`q = 1 - p`

`q = 1 - 0.15`

`q = 0.85`

The required probability implies that:

The first person did not fail: i.e. 0.85

The second person did not fail: i.e. 0.85

The third person failed: i.e. 0.15

This is then calculated as:

`Probability = 0.85 * 0.85 * 0.15`

`Probability = 0.108375`

Hence, the probability that the first false positive occurred at the third person is 0.108375