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 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?

Answer 1

Answer:0.741

Step-by-step explanation:

Given

Probability that lie detected as lie is 65 %

Probability that Truth detected as lie is 14 %

Probability that People telling Truth P(Telling Truth)=93 %

P(Telling Lie)=7%

$P(Person\ is\ telling\ truth|but\ fails\ the\ test)=\frac{P(Telling\ Truth\ but\ fails\ test)}{P(fails\ test)}$

P(Person is telling truth|but fails the test)$=\frac{P(Telling\ Truth)\times P(Truth\ as\ lie)}{P(Telling\ Truth)\times P(Truth as lie)+P(Telling\ Lie)\times P(Lie\ as\ lie)}$

$=\frac{0.93\times 0.14}{0.93\times 0.14+0.07\times 0.65}$

$=\frac{0.1302}{0.0455+0.1302}=0.741$