All athletes at the Olympic games are tested for performance-enhancing steroid drug use. The imperfect test gives positive resul
ts (indicating drug use) for 90% of all steroid-users but also for 2% of those who do not use steroids (that is, the false-positive rate is 2%). Suppose that 4% of all registered athletes use steroids. If an athlete is tested negative, what is the probability that the test is wrong and he or she actually uses steroids?