Some employers use lie detector tests to screen job applicants.Lie detector tests are not completely reliable.Suppose that a polygraph can detect 64% of lies,but incorrectly identifies 16% of true statements as lies.A company gives its job applicants a polygraph test,asking "Did you tell the truth on your job application?".All the applicants answer "Yes",but the test identifies some of those answers as lies,thereby causing the person to fail the test.Suppose that 90% 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)0.444
B)0.308
C)0.16
D)0.692
E)0.9

Question

Quizplus · Accepted Answer

To find the probability that a person who fails the test was actually telling the truth, use Bayes' theorem. Let T be the event of telling the truth, and F be the event of failing the test. We need P(T|F). Given: P(T) = 0.9, P(F|T) = 0.16, P(F|L) = 0.64, and P(L) = 0.1. P(F) = P(F|T)P(T) + P(F|L)P(L) = 0.16*0.9 + 0.64*0.1 = 0.208. Then, P(T|F) = P(F|T)P(T) / P(F) = 0.16*0.9 / 0.208 = 0.692.

Some Employers Use Lie Detector Tests to Screen Job Applicants