Question

Most states in the u.s. ban the use of polygraph ("lie-detector") in their justice systems. false positives (where an individual fails even though he or she is telling the truth) are relatively common and make up about 15% of all test results. (a) if 8 random people take a polygraph test, what is the probability that none of the results are false positive?

Answer 1

The problem states that 15% of the result are false positive, but it asks about for results that are not false positive, so we should focus on 85% or .85 to express it as a probability value. Then the problem ask about 8 random people taking the test, since it is not mentioned that the results of the test are connected in some way we can assume that they are independent. In that case we can solve it by .85^8, which is .27. The result is 27% of probability