Consider a test for using a particular drug. The test will produce 99% true positive results for drug users and 99% true negative results for non-drug users. Suppose that 0.5% of people are users of the drug. What is the probability that a randomly selected individual with a positive test is a drug user?

Step-by-step explanation:

Using  Bayes' theorem, we have:

is a conditional probability: the likelihood of event A occurring, given that B is true.

is also a conditional probability: the likelihood of event B occurring, given that A is true.

P(A) and P(B) are the marginal probabilities of observing A and B, independently of each other.

We solve thus:

                 =

                 =

                 =

                 =

                 = or %

Therefore, if an individual tests positive, it is more likely than not (1 - 33.2% = 66.8%) that they do not use the drug.

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step-by-step explanation:

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