All athletes at the olympic games are tested for performance-enhancing steroid drug use. the imperfect test gives positive results (indicating drug use) for 90\% of all steroid-users but also (and inc

All athletes at the olympic games are tested for performance-enhancing steroid drug use. the imperfect test gives positive results (indicating drug use) for 90\% of all steroid-users but also (and incorrectly) for 2\% of those who do not use steroids. suppose that 5\% 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?