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)0.349
B)0.14
C)0.741
D)0.259

Question

Quizplus · Accepted Answer

0.741To find the probability that a person who fails the test was actually telling the truth, we use Bayes' theorem. Let's denote T as the event of telling the truth and F as the event of failing the test. We need to find P(T|F), the probability of telling the truth given that the person failed the test.Given:- P(F|T) = 0.14 (probability of failing the test given the person told the truth)- P(T) = 0.93 (probability of telling the truth)- P(F|~T) = 0.65 (probability of failing the test given the person lied)- P(~T) = 0.07 (probability of lying, which is 1 - P(T))We can calculate P(F), the total probability of failing the test, using the law of total probability:P(F) = P(F|T)P(T) + P(F|~T)P(~T)     = 0.14*0.93 + 0.65*0.07     = 0.1302 + 0.0455     = 0.1757Now, using Bayes' theorem:P(T|F) = [P(F|T)P(T)] / P(F)       = (0.14*0.93) / 0.1757       = 0.1302 / 0.1757       ≈ 0.741Therefore, the probability that a person who fails the test was actually telling the truth is approximately 0.741.

Some Employers Use Lie Detector Tests to Screen Job Applicants