The known rate of usage of a particular illicit drug is 3%. A test exists that will correctly identify a drug user 96% of the time. The test also misidentifies a non-user 2% of the time. What is the probability that a person who has tested positive for the drug is actually a non-user?

Question

kropot72 · Answer

The probability that the person is a user is 0.03.
The probability of a correct test result is 0.96
The probability of  misidentifying a non-user is 0.02
The probability that a person who has tested positive for the drug is actually a non-user is a compound event. The compound event is made up of three separate and independent sub-events. Therefore the probability of the compound event is the product of the separate probabilities of each sub-event.
Required probability = 0.03 * 0.96 * 0.02 = 0.000576