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Lie detectors are controversial​ instruments, barred from use as evidence in many courts.​ Nonetheless, many employers use lie detector screening as part of their hiring process. There has been some​ research, but no​ agreement, about the reliability of polygraph tests. Based on this​ research, suppose that a polygraph can detect 61​% of​ lies, but incorrectly identifies 16​% of true statements as lies. A company believes that 95​% of its job applicants are trustworthy. The company gives everyone a polygraph​ test, asking​ "Have you ever stolen anything from your place of​ work?" Naturally, all the applicants answer​ "No," but the polygraph identifies some of those answers as​ lies, making the person ineligible for a job.

a) Here is the outline of a probability tree for this situation. Fill in the probabilities.


b) What is the probability that a random job applicant will be an honest worker who is cleared by the​ polygraph?

P(Honest Cleared)  = 0.95 * 0.84   =  0.798

​c) What is the probability that a job applicant who is rejected by the polygraph was actually dishonest​?

(0.61 * 0.05)/(0.95 * 0.16 + 0.05 * 0.61)  =  0.1671


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