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

To 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(F|~T) = 0.65 (probability of failing the test given the person lied)- P(T) = 0.93 (probability of telling the truth)- P(~T) = 0.07 (probability of lying, which is 1 - P(T))Using Bayes' theorem:$$P(T|F) = \frac{P(F|T) \cdot P(T)}{P(F|T) \cdot P(T) + P(F|~T) \cdot P(~T)}$$Substituting the given values:$$P(T|F) = \frac{0.14 \cdot 0.93}{0.14 \cdot 0.93 + 0.65 \cdot 0.07}$$$$P(T|F) = \frac{0.1302}{0.1302 + 0.0455}$$$$P(T|F) = \frac{0.1302}{0.1757} \approx 0.741$$Therefore, 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