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, 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. What is the probability that a machine will conclude that each of the three employees is lying when all are telling the truth? 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?
-This section of the book is about the multiplicative law of probability and the additive law of probability.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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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