A test for a certain drug produces a false negative 3% of the time and a...

A test for a certain drug produces a false negative 3% of the time and a false positive 9% of the time. Suppose 12% of the employees at a certain company use the drug. If an employee at the company tests negative, what is the probability that he or she does use the drug?

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Expert Solution

TN : Test Negtive

TP : Test positive

D: uses the drug

: does not use the drug

False Negative : Test Negative when he or she does use drug = 3%

P(TN|D) = 3/100 =0.03

False positive : Test Positive when he or she does not use drug = 9%

P(TP|) = 9/100 =0.09

P(TN|) = 1 -P(TP|)=1-0.09 =0.91

Suppose 12% of the employees at a certain company use the drug

P(D) = 12/100 =0.12

P()=1-0.12 =0.88

If an employee at the company tests negative, probability that he or she does use the drug = P(D|TN)

P(D)P(TN|D) = 0.12 x 0.03 = 0.0036

P()P(TN|) = 0.88 x 0.91 = 0.8008

If an employee at the company tests negative, probability that he or she does use the drug = 0.004475385

orchestra answered 1 year ago

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