Question

A company requires all job applicants to undergo drug testing for employment. If the applicant has used drugs the test has a 90% chance of a positive result. If the applicant has not used drugs the test has an 85% chance of a negative result. 4% of all applicants have used drugs. If an applicant has a positive test, what is the probability he or she has actually used drugs?

Answer 1

Bayes' theorem: P(A | B) = P(A & B)/P(B)

P(used drugs) = 0.04

P(did not use drugs) = 1 - 0.04 = 0.96

P(used drugs | positive) = P(used drugs and positive) / P(positive)

= P(used drugs and positive) / [P(used drugs and positive) + P(did not use drugs and positive)]

= (0.04x0.90) / (0.4x0.90 + 0.96x0.15)

= 0.2