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(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