A drug testing company advertises a test for steroids that is 93.5% effective at detecting steroid use. It has a true negative effectiveness of 93.5%. Suppose 8% of 10,000 professional cyclists are believed to be using steroids.

Suppose the haplessly named Lance Robustcalve tests positive for steroid use. What is the probability that he's really not using steroids?

2 answers

p = 100% - 8% = 92% = 0.92 = 92/100 = 23/25.
It doesn't matter how many others are using. You just want the probability that his test is false positive.

p = 100% - 93.5% = ?