Lie detectors are sometimes used in criminal investigations, but they do not fun

Question

Lie detectors are sometimes used in criminal investigations, but they do not function perfectly. If a suspect is guilty, there is a 0.8 chance that the lie detector will detect guilt. If a suspect is not-guilty, there is a 0.2 chance that it will (wrongly) detect guilt. Assume that 20% of all suspects are guilty. Use Bayes Rule to answer the following questions:<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

(a) In the investigation of a single suspect, if the lie detector detects guilt, how likely is it that the suspect is guilty? Do you think that the evidence of the lie detector should be relied upon in the investigation?

(b) Now assume that a certain gang containing ten members is under suspicion of a crime. Assume that the probability of the gang being guilty of the crime is 20% (since other gangs are also under suspicion). Each member of the gang is independently subjected to the lie detector, and guilt is detected in five out of ten. How likely is it that the gang is guilty?

(c) How many of the ten gang members would need to "fail" the lie-detector in order for you to be 99% sure of the gang's guilt?

Explanation / Answer

Some employers use lie detector tests to screen applicants.Lie detector tests are not completely reliable.Suppose that in a lie detector test,64% of lies are identifies as lies and that 17% of true statements are also identified as lies.A company gives job applicants a polygraph test,asking, "Did you tell the truth on your job application?Suppose that 94% of the job applicants tell the truth during the polygraph test.What is the probability that a person who fails the test was actually telling the truth?

sol :P[telltruth& fail test] = 17% of 94% = 15.98% = A

P[lie & fail test] = 64% of 6% = 3.84% = B
P[fail test] = A+B = 19.82% = C

P[telling truth | fails test] = A/C
= 0.8063

this might help..........!!!

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