Question

5) Suppose hospital employees are required to take lie detector tests. Suppose that the probability is 0.05 that the lie detector concludes that a person is lying who, in fact, is telling the truth. Suppose that any pair of tests is independent.

a) What is the probability that the lie detector will conclude that each of three employees is lying when all are telling the truth?
b) What is the probability that the lie detector will conclude that at least one of three employees is lying when all are telling the truth?

Answer 1

a)Binomial Problem with n = 3 and p = 0.05

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

b) P(at least one true) = 1 - P(says zero are lying when all tell truth)

= 1 -0.95^3

= 0.1426

Explanation: