Suppose that $8\%$ of all bicycle racers use steroids, that a bicyclist who uses steroids tests positive for steroids $96\%$ of the time, and that a bicyclists who does not use steroids tests positive for steroids $1\%$ of the time.
(a) What is the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids?
(b)What is the probability that a randomly selected bicyclist who tests negative for steroids actually uses steroids?
I have idea of part a) of this problem. I got answer as 0.893 but I am not able to change it for negative test. Please help how to proceed
Best Answer
Hint
If you need Bayes' theorem equation for this, you haven't fully grasped it, and you should fall back on a more intuitive approach
Uses steroids $(8\%)\rightarrow$ tests negative $(4\%)\rightarrow$ P(uses steroids $\cap$ tests negative) = ...
Doesn't use steroids $(92\%)\rightarrow$ tests negative $(99\%)\rightarrow$ P(Doesn't use steroids $\cap$ tests negative) =
I think you should be able to continue from here
Or it seems that you can't !