Apolicy requiring all hospital employees to take lie detector tests may reduce losses due to theft, but some employees regard such tests as a violation of their rights. Past experience indicates that lie detectors have accuracy rates that vary from 92% to 99%.2 To gain some insight into the risks that employees face when taking a lie detector test, suppose that the probability is. 05 that a lie detector concludes that a person is lying who, in fact, is telling the truth and suppose that?

suppose that any pair of tests are independent. What is the probability that a machine will conclude that

a each of three employees is lying when all are telling the truth?

b at least one of the three employees is lying when all are telling the truth?

Answer:

a. The probability that each of three employees is lying when all are telling the truth is 0.000125

b. The probability that at least one of the three employees is lying when all are telling the truth is 0.1426

Step-by-step explanation:

Let the event be;

A = the lie detector concludes that a person is lying who, in fact, is telling the truth

B = the lie detector concludes that a person is lying who, in fact, is telling lie

Given their probabilities as:

P (A) = 0.05 and P (B) = (1 - 0.05) = 0.95

a. What is the probability that a machine will conclude that each of three employees is lying when all are telling the truth?

A binomial problem with n = 3 and P = 0.05

P (all are telling truth) = P^n = 0.05^3 = 0.000125

b. What is the probability that at least one of the three employees is lying when all are telling the truth?

P (at least one is telling) = P (one is telling lie) + P (two are telling lie) + P (three are telling lie)

Or

P (at least one is telling) = 1 - P (B) = 1 - (0.95) ^3 = 0.1426