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

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)=(P(Telling\ Truth\ but\ fails\ test))/(P(fails\ test))`

P(Person is telling truth|but fails the test)
`=(P(Telling\ Truth)* P(Truth\ as\ lie))/(P(Telling\ Truth)* P(Truth as lie)+P(Telling\ Lie)* P(Lie\ as\ lie))`

`=(0.93* 0.14)/(0.93* 0.14+0.07* 0.65)`

`=(0.1302)/(0.0455+0.1302)=0.741`