the known rate of usage of a particular illicit drug is 3% (a random sample of the population would find that 3% of the people are currently using the drug.) a test exists that will correctly identify a drug user 96% of the time. the test also misidentifies a non user (a false positive) 2% of the time. what is the probability that a person who has tested posiitive for the drug is actually a non-user.

Question

the known rate of usage of a particular illicit drug is 3% (a random sample of the population would find that 3%  of the people are currently  using the drug.) a test exists that will correctly identify a drug user 96% of the time. the test also misidentifies a non user (a false positive) 2% of the time. what is the probability that a person who has tested posiitive for the drug is actually a non-user.

anonymous · Answer

So for a randomly selected individual, the chance that they'll test positive is:
.03*.96 + .97*.02 = .0482
(that's true positives plus false positives)

The chance of getting a false positive is:
.97*.02 = 0.0194

so, given that someone tests positive, the chance that it's a false positive is:
.0194/.0482 = .4025 = 40.25%