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
please revert for any clarification