Some employers use lie detector tests to screen job applicants. Lie detector tests are not completely reliable. Suppose that in a lie detector test, 65% of lies are identified as lies and that 14% of true statements are also
Identified as lies. A company gives its job applicants a polygraph test, asking "Did you tell the truth on your job
Application?". Suppose that 93% 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?
A) 0.741
B) 0.14
C) 0.259
D) 0.349

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the probability that a person who fails the test was actually telling the truth is calculated as follows: P(True | Fail) = [P(Fail | True) * P(True)] / P(Fail). P(Fail | True) = 0.14, P(True) = 0.93, and P(Fail) = P(Fail | True) * P(True) + P(Fail | Lie) * P(Lie) = 0.14 * 0.93 + 0.65 * 0.07 = 0.1953. Therefore, P(True | Fail) = (0.14 * 0.93) / 0.1953 = 0.741.

Some Employers Use Lie Detector Tests to Screen Job Applicants