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) 0.259
C) 0.349
D) 0.14

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(T|F) = [P(F|T) * P(T)] / P(F). Here, P(F|T) = 0.14, P(T) = 0.93, and P(F) = P(F|T) * P(T) + P(F|L) * P(L) = 0.14 * 0.93 + 0.65 * 0.07. Solving this gives approximately 0.741.

Some Employers Use Lie Detector Tests to Screen Job Applicants