VD [20 points Lie Detector Test: There is a 72% chance hat a polygraph lie delec

Question

VD [20 points Lie Detector Test: There is a 72% chance hat a polygraph lie delecter leg will catch a per on who is ia fact lying. Furthermoee, dere-s appros mately a 7% chance that polygraph will they accuse snome of lyng. a Suppose that a person aswers 90%ofalong batiry ofquestions truthfully what Percent geofanners will the polygraph wrewgly indicate are Nes? b. Suppose that a person answers 10% of along battery of questions with lies What percentage of answers will the polygraph earnecitly indicate are Ne? Repeat partia) and

Explanation / Answer

V.

Let

L = polygraph says lie
T = person is stating the truth

a)

P(T n L) = P(T) P(L|T) = 0.90*0.07 = 0.063 = 6.3% [ANSWER]

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b)

P(T' n L') = P(T') P(L|T') = 0.10*0.72 = 0.072 = 7.2% [ANSWER]

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c)

PART A:

P(T n L) = P(T) P(L|T) = 0.50*0.07 = 0.035 = 3.5% [ANSWER]

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PART B:

P(T' n L') = P(T') P(L|T') = 0.50*0.72 = 0.036 = 3.6% [ANSWER]

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