(False Positive) A company believes 95% of its jobs applicants are trustworthy.
ID: 3355104 • Letter: #
Question
(False Positive) A company believes 95% of its jobs applicants are trustworthy. The company gives everyone a polygraph test, asking “have you ever stolen anything from your workplace”, to which all applicants naturally answer no. The company then uses a polygraph (lie detector) to see if they are trustworthy. Suppose when a person lies, the polygraph detects the lie with probability 65%, but incorrectly identifies 15% of true statements as lies. What is the probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy?
Explanation / Answer
probability that a job applicant rejected under suspicion of dishonesty =P(trustworthy but rejected +untrustworthy and rejected) =0.95*0.15+(1-0.95)*0.65=0.175
therefore probability that a job applicant rejected under suspicion of dishonesty was actually trustworthy
=P(trustworthy but rejected)/P(rejected) =0.95*0.15/0.175=0.8143
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.