(10 points) 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

If an employee at the company tests negative, the probability that he or she does use the drug is P=0.58.

Step-by-step explanation:

We have this information:

proportion of drug users P(D)=0.12

false negatives FN=P(N|D)=0.03 --> True negatives P(N|ND)=0.97

false positives FP=P(P|ND)=0.09 --> True positives P(P|D)=0.91

where:

D: drug user

ND: no drug user

N: negative result

P: positive result

We have to calculate the probability that, given a positive teste, the person is a drug user.

Applying the Bayes theorem, we have:

where is the figure

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: