After winning a race, an Olympic runner is tested for the presence of steroids. The test comes up positive, and the athlete is accused of doping. Suppose it is known that 5% of all victorious Olympic runners do use performance-enhancing drugs. For this particular test, the probability of a positive finding given that drugs are used is 95%.

The probability of a false positive is 2%. What is the (posterior) probability that the athlete did in fact use steroids, given the positive outcome of the test?