The imperfect test gives positive results (indicating drug use) for 80% of all interns who actually use drugs but also (incorrectly) for 3% of those who do not use drugs. Suppose that only 10% of all of these interns actually use drugs. If an intern is tested negative, what is the probability that he/she uses drugs

The probability that an uses drugs given that the result was negative is 0.0224.

Step-by-step explanation:

Let's denote the events as follows:

D = an intern uses drugs.

X = the test result was positive.

The information provided is:

Compute the probability that the test result of an intern is positive as follows:

The probability that the test result of an intern is positive is P (X) = 0.107.

Compute the probability that the result is negative given that he/she uses drugs as follows:

Compute the probability that an uses drugs given that the result was negative as follows:

Thus, the probability that an uses drugs given that the result was negative is 0.0224.