Question

Question Help Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lle detector screening as part of their hiring process. There has been some research, but no agreement, about the reliability of polygraph tests. Based on this research, suppose that a polygraph can detect 62% of lies, but incorrectly identifies 11% of true statements as lies. A company believes that 96% of its job applicants are trustworthy. The company gives everyone a polygraph test, asking "Have you ever stolen anything from your place of work?" Naturally, all the applicants answer "No," but the polygraph identifies some of those answers as lies, making the person ineligible for a job. -0.89 -0.62 -0.38 (Type integers or decimals. Do not round.) Polygraph says "Doesn't Lie" Polygraph says "Lie" Polygraph says 'Doesn't Lie" -0.04_Dishonest b) What is the probability that a random job applicant will be an honest worker who is cleared by the polygraph? The probability that a random job applicant is an honest worker who is cleared by the polygraph is (Type an integer or a decimal. Do not round.) c) What is the probability that a job applicant who is rejected by the polygraph was actually dishonest? The probability that a job applicant who is rejected by the polygraph was actually dishonestis (Round to four decimal places as needed.) Enter your answer in each of the answer boxes.

Answer 1

b)We have to find

P( honest worker I  cleared by the polygraph)

= P( cleared by polygraph I honest worker ) *P( honest worker) / P(cleared by polygraph) ( using Bayes' theorem)

P(cleared by polygraph) = P( cleared by polygraph I honest worker ) *P( honest worker)

+ P( cleared by polygraph I dishonest worker ) *P( dishonest worker)

=0.89 * 0.96 + 0.38*0.04

= 0.8544 +0.0152

=0.8696

thus, P( honest worker I  cleared by the polygraph) =0.8544/ 0.8696= 0.9825

Probability that a random worker is a honest worker who is cleared by polygraph = 0.9825

c)We have to find

P( dishonest worker I rejected by polygraph)

=P( rejected by polygraph I dishonest worker ) *P( dishonest worker) / P(rejected by polygraph) ( using Bayes' theorem)

P(rejected by polygraph) = P( rejected by polygraph I honest worker ) *P( honest worker)

+ P( rejected by polygraph I dishonest worker ) *P( dishonest worker)

=0.11 * 0.96 + 0.62*0.04

=0.1304

thus, P( dishonest worker I  rejected by the polygraph) =(0.04*0.62) / 0.1304= 0.1902

Probability that a random worker is dishonest who is rejected by polygraph = 0.1902