Question

An article states that false-positives in polygraph tests (tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 10% of the time. Suppose that such a test is given to 10 trustworthy individuals. (Round all answers to four decimal places.) What is the probability that all 10 pass?

Answer 1

0.3487 or 34.87%

Explanation:

If false-positives occurs about 10% of the time, it means that polygraph tests are accurate around 90% of the time.

That is, the probability that the polygraph does not give a false-positive is 0.9

Since the result given by the polygraph to a given question is independent from the responses to any previous question (or it should be), then the probability that the polygraph does not give a false-positive 10 times in a row with 10 people that are telling the truth is

`\large (0.9)^(10)=0.3487` or 34.87%