Suppose hospital employees are required to take lie detector tests. Suppose that
ID: 3300780 • Letter: S
Question
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?Explanation / Answer
Here we are given that the probability that the test gives lie even when the person is telling the truth is 0.05. Therefore,
P( Test lying | Truth ) = 0.05
a) Probability that the lie detector will conclude that each of the three employees is lying when all are telling the truth is computed as:
= P( Test lying | Truth ) *P( Test lying | Truth ) *P( Test lying | Truth )
= 0.053
= 0.000125
Therefore 0.000125 is the required probability here.
b) Probability that the lie detector will conclude that at least one of the three employees is lying when are all telling the truth
= 1 - Probability that the lie detector will conclude that all of the three employees are telling truth when are all telling the truth
= 1 - (1 - 0.05)3
= 0.142625
Therefore 0.142625 is the required probability here.