The organizers of a cycling competition know that about 8% of the racers use steroids. They decided to employ a test that will help them identify steroid-users. The following is known about the test: When a person uses steroids, the person will test positive 96% of the time; on the other hand, when a person does not use steroids, the person will test positive only 9% of the time. The test seems reasonable enough to the organizers. The one last thing they want to find out is this: Suppose a cyclist does test positive, what is the probability that the cyclist is really a steroid-user.
S be the event that a randomly selected cyclist is a steroid-user and P be the event that a randomly selected cyclist tests positive.
***My questions is Can someone please translate and explain P(P|S) and P(S|P) ?