Bayes Theorem Problems 1. In a lie-detector test, an individual is asked to answ

Question

Bayes Theorem Problems 1. In a lie-detector test, an individual is asked to answer a series of questions while connected to a polygraph machine. This instrument measures and records several physiological responses of the individual on the basis that false answers will produce distinctive measurements. Assume that 99% of the individuals who go in for the polygraph test tell the truth. These tests are consideredto be 95% reliable. In other words, there is a 95% chance that the test will detect a lie if an individual actually lies. Let there also be a 0.5% chance that the test erroneously detects a lie even when the individual is telling the truth. An individual has just taken the polygraph and the test detected a lie. What is the probability that the individual was actually telling the truth? eat th robilty that

Explanation / Answer

Probability of speaking truth = 0.99

P(detect a lie |if lie is spoken) = 0.95

P(detect a lie |if lie is not spoken) = 0.005

P(telling the truth | detected a lie)

= P(telling the truth and detected a lie) / P(detected a lie)

= 0.99 *0.005 /( 0.01 * 0.95 + 0.99 * 0.005)

=0.3425605

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