Probability - What is the probability that a randomly selected bicyclist who tests negative for steroids actually uses steroids 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
 A: 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 !

P(uses steroids $\cap$ tests negative) = $0.32\%$
P(doesn't use steroids $\cap$ tests negative) = $91.08\%$
P(uses steroids | tests negative) = $\dfrac{0.32}{0.32+91.08}$

A: Pictorial solution. In every diagram but the topmost, we are working in a population of 10000 people to boost intuition.

A: You were able to solve this problem correctly:

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 bicyclist 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?

So now try solving this problem:

Suppose  that  $8\%$  of  all  bicycle  racers  use  steroids,  that  a  bicyclist  who  uses  steroids  tests  negative  for steroids $4\%$ of the time, and that a bicyclist who does not use steroids tests negative for steroids $99\%$ of the time.
(b)What is the probability that a randomly selected bicyclist who tests negative for steroids actually uses steroids?

As you can see, it's the exact same problem, except that the word "positive" is changed to "negative" and a couple of the numbers are different.
(This is simply a more explicit exposition of the hint you received in a comment from Stan.)
