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A polygraph can detect 63% of lies but incorrectly identifies 16% if true statem

ID: 3358695 • Letter: A

Question

A polygraph can detect 63% of lies but incorrectly identifies 16% if true statements as lies. A company gives applicants a polygraph test. All the applicants give the same answer, but the test says some are lying. 94% of the applicants are being truthful. What’s the probability that a person who fails the test is telling the truth? Use a tree diagram to determine your answer. A polygraph can detect 63% of lies but incorrectly identifies 16% if true statements as lies. A company gives applicants a polygraph test. All the applicants give the same answer, but the test says some are lying. 94% of the applicants are being truthful. What’s the probability that a person who fails the test is telling the truth? Use a tree diagram to determine your answer.

Explanation / Answer

let probbaility of being truthful=P(T)=0.94

and probability of telling lie=P(L)=1-0.94=0.06

probability of test saying person is telling lie =P(TL)

probability of test saying person is truthful =P(TT)

from above P(TL|L)=0.63

and P(TL|T)=0.16

probability that person fails the test =P(TL)=P(T)*P(TL|T)+P(L)*P(TL|L)=0.94*0.16+0.06*0.63=0.1882

therefore  probability that a person who fails the test is telling the truth =P(T|TL)=P(T)*P(TL|T)/P(TL)

=0.94*0.16/0.1882=0.7991

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