Question 651093
A policy requiring all hospitals to take lie detector tests may reduce losses due to theft, but some employees regard such tests as a violation of their rights. Reporting on a particular hospital that uses this procedure, the Orlando Sentinel Star (August 3, 1981) 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, 
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suppose that the probability is .05 that a particular lie detector concludes that a person is lying who, in fact, is telling the truth, and suppose that any pair of tests are independent. 
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What is the probability that a machine will conclude that each of the three employees is lying when all are telling the truth? 
Binomial Problem with n = 3 and p = 0.05
P(all telling truth) = 0.05^3 = 0.000125
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What is the probability that the machine will conclude that at least one of the three employees is lying when all are telling the truth?
P(at least one true) = 1 - P(says zero are lying when all tell truth)
= 1 -0.95^3
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= 0.1426
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Cheers,
Stan H.
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