Question

It is well known that steroid usage is banned in athletes. As a result, athletes are randomly tested. The steroid test procedures are believed to be equally effective on both steroid users as well as non-steroid users. The effective rate is 98%. Assume 90% of the athletes are clean (not steroid users). Suppose an athlete is tested as a steroid user (and thus could be disqualified from the Summer Olympics games), what is the probability that the athlete is actually clean (i.e., not a steroid user)

Answer 1

18% that the athlete is disqualified but is actually clean

Explanation:

In order to find the probability of two events happening together, in this case the athlete being disqualified and being clean, we need to multiply the probabilities. So,

It is a 90% chance that the athlete is clean and a 2% chance that the test fails so multiply the two

.9 * .2 = .18

This means that it is an 18% chance that the athlete is clean but is still disqualified.