Question

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 job applicants tell the truth during the polygraph test. What is the probability that someone who fails the test was actually telling the truth.

Answer 1

The probability is 0.7410

Explanation:

Let's call: L the event in which a job applicant lies, T the even in which a a job applicant tell the truth and F the event in which the job applicant fails the test.

So, the probability P(T/F) that someone who fails the test was actually telling the truth is calculated as:

P(T/F) = P(T∩F)/P(F)

Where P(F) = P(T∩F) + P(L∩F)

Then, P(T∩F) is the probability that someone tells the truth and fails the test. It is given by the multiplication of the proportion of job applicants that tell the truth with the proportion of true statements that are identified as lies. This is:

P(T∩F) = 0.93 * 0.14 = 0.1302

At the same way, P(L∩F) is the probability that someone lies and fails the test. It is given by the multiplication of the proportion of job applicants that lies with the proportion of lies that are identified as lies. This is:

P(L∩F) = 0.07 * 0.65 = 0.0455

So, P(F) is calculated as:

P(F) = 0.1302 + 0.0455 = 0.1751

Finally, the probability P(T/F) that someone who fails the test was actually telling the truth is:

P(T/F) = 0.1302/0.1757

P(T/F) = 0.7410