Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of the hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no agreement, about reliability of polygraph tests. Based on the research, suppose a polygraph can detect 65% of lies, but incorrectly identifies 15% of true statements as lies.
A certain company believes 95% of job applicants are trustworthy. The company gives everyone a polygraph test asking, "Have you ever stolen anything from your work place?" Naturally, all applicants answer "No", but the polygraph identifies some of the answers as lies, making the person ineligible for a job. What is the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy?
A) 0.143
B) 0.618
C) 0.333
D) 0.814