1. The problem statement, all variables and given/known data The proportion of people in a given community who have a certain disease is 0.005. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.98. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02. If a person tests negative, what is the probability that the person actually has the disease? 2. Relevant equations I'm at a loss for the relevant equation. I've scanned through my book several times. 3. The attempt at a solution I set the problem up as follows: Given the following: Probability that one has the disease: P(D)=.005 Probability that given one has the disease, they test positive: P(+|D)=0.98 Probability that given one does not have the disease, they test positive: P(+|D^c)=.02 I've used the notation P(-) for test is negative which is equal to P(+^c) I'm trying to find P(D|-) based on the problem statement. I can't find any way to relate this to what I've been given. The solution says to use P(+|D^c)P(D)=.02*.005=1.0E-4 but I have no idea where that relation came from or where to find a proof of such online. If anyone could explain to me why P(D|-)=P(+|D^c)P(D) it would really help my understanding of the problem.