25...A policy requiring all hospital employees to take lie detector tests may re

Question

25...A policy requiring all hospital employees to take lie detector tests may reduce the losses due to theft but some employees regard such actions as a violation of their rights. Reporting on a particular hospital that uses this procedure, a local newspaper notes that lie detectors have accuracy rates that vary from 92% to 99%. To gain some insight into the risks that employees face when taking a lie detector test, suppose that the probability is 0.06 that a particular lie detector concludes that a person is lying who, in fact, is telling the truth and suppose that all tests are independent. Suppose that 4 employees are selected at random. What is the probability that the machine will conclude that at least one of the 4 employees is lying when all of them are telling the truth?

Explanation / Answer

from above question we get that probabilty of lie detector concluding that a person is lying when he is telling the truth =0.06

hence  probability that the machine will conclude that at least one of the 4 employees is lying when all of them are telling the truth =1- P(it conclude that none is lying) =1- (1-0.06)4 =1-0.7807 =0.2193

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