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?
To simplify the expression, we are going to need to rewrite the expression by expanding the terms and then solve by using the distributive property. Then we combine like terms in till the expression can no longer be simplified to find our answer.