Assume that we have the same amount of females and males and they go through a screening process. At the end it turns out that 5% men are positive, and 0.25% women are positive. If a person is picked randomly and that person is HIV positive what is the probability that he is a male?
Is the way to think about this and do it something along the lines of:
Firstly there are the same amount of females and males so the probability of picking a male is 0.5. Next, within that group of males, 5% are positive. So our probability of picking a HIV positive male is 2.5%?