Suppose there are a village which have 2% citizen who have AIDS and there are a system which is used to check the citizen who have AIDS or not.The result of check have 5% possible error.A man had been checked and his checked report show that he is a carrier. Find the probability of the man who doesn't has AIDS.
P(The man does not have AIDS | Checking is positive)
=P(The man does not have AIDS and Checking is positive) / P(Checking is positive)
= 0.98 x 0.05 / (0.98 x 0.05 + 0.02 x 0.95)