Question

Suppose you have data that shows that 12% of athletes test positive for steroids. You also know that 11% of athletes test positive for steroids and actually use steroids. What is the probability that an athlete uses steroids, given that he tests positive?

Answer 1

Let
\(T\)=test positive for steroids
\(S\)=actually use steroids.

Then you have that:
\(P(T)=0.12\)
\(P(T \cap S)=0.11\)

And we need to find \(P(S|T)\)

does this make sense?