A person is going to take a lie detector test. The probability that a subject is

Question

A person is going to take a lie detector test. The probability that a subject is telling the truth on the test is 80%. If a subject is lying then the test is fairly effective, and detects the lie (returns a “positive”) 88% of the time, according to studies. If a person is not lying, the studies show that the test correctly returns a “negative” with probability 86%. What is the probability that a subject is lying given the lie-detector test is positive (if we take the results of the studies as facts)? For notational ease, in your answer please let L be the event that the subject is lying and let N be the event that the lie-detector test comes up negative (indicates that the subject is telling the truth).

Explanation / Answer

Probability that a subject is telling the lie on the test = 0.2 (L)

Subject is lying then the test is fairly effective, & detects the lie = 0.88

Probability that a subject is lying given the lie-detector test is positive = 0.2 x 0.88 = 0.176

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