Pre-Employment Drug Screening Results are shown in the following Table: Positive Test Result Negative Test Result Subject Uses Drugs 8 (True...

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Pre-Employment Drug Screening Results are shown in the followingTable:
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 theprobability that the subject had a positive test result, given thatthe subject actually uses drugs. That is,
(positive test result subject uses drugs).
If 1 of the 200 test subjects is randomly selected, find theprobability that the subject actually uses drugs, given that he orshe had a positive test result. That is,
(subject uses drugs ).

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4.2 Ratings (816 Votes)

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

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8/10

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.8

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

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8/18

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 4/9 or 0.444

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