Answer:
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:
[tex]P(D|P)=\frac{P(D)*P(P|D)}{P(D)*P(P|D)+(1-P(D))*P(P|ND)}\\\\\\P(D|P)=\frac{0.12*0.91}{0.12*0.91+(1-0.12)*0.09}=\frac{0.1092}{0.1092+0.0792}=\frac{0.1092}{0.1884}\\\\\\P(D|P)= 0.58[/tex]
