Question

Pre-Employment Drug Screening Results are shown in the following Table:

	Positive Test Result	Negative Test Result
Subject Uses Drugs	8 (True Positive)	2 (False Negative)
Subject is not a Drug User	10 (False Positive)	180 (True Negative)

If 1 of the 200 test subjects is randomly selected, find the probability that the subject had a positive test result, given that the subject actually uses drugs. That is,

(positive test result subject uses drugs).

If 1 of the 200 test subjects is randomly selected, find the probability that the subject actually uses drugs, given that he or she had a positive test result. That is,

(subject uses drugs ).

Answer 1

a) P(positive test result | subject uses drugs) = P(positive test result and subject uses drug) / P(subject uses drug)

                                                                 = (8/200) / ((8+2)/200)

                                                                 = 8/10

                                                                 = 0.8

P(subject uses drug | positive test result) = P(subject uses drug and positive test result) / P(positive test result)

                                                          = (8/200) / ((8+10)/200)

                                                          = 8/18

                                                          = 4/9 or 0.444