1. The problem statement, all variables and given/known data Suppose there are two different diagnostic tests (say test A and test B) for some disease of interest. Assume that the prevalence of this disease in a large population is 1%. Test A has a false negative rate of 10% (false negative means that the test result is negative when the test is applied to a person who has the disease). Similarly, the false negative rate of test B is 5%. The false positive rate of test A is 4% (false positive means that the test result is positive even though it is applied to a person who does not have the disease). Similarly, the false positive rate of test B is 6%. If both tests A and B are positive when administered to a person selected at random from the population, what is the probability this person has the disease? 2. Relevant equations P(A|B)=P(A intersect B)/P(B) for conditional probability P(B|A)=(P(A|B)*P(B))/P(A) for Bayes' Rule 3. The attempt at a solution I have written down all of the outcomes for Tests A and B. For Test A, I have P(-|+)= Probability that the test results are negative when test is applied to someone who has the disease=.10. Similarly, I have P(+|-)=.04. Therefore P(+|+)=1-.10=.90 and P(-|-)=1-.04=.96. For Test B, I have P(-|+)=.05, P(+|-)=.06, P(+|+)=.95, and P(-|-)=.94. My question is that I'm not sure what to do now. It seems as if you should do the following: Let P(A)=Probability of population who have the disease, and let P(B)=Probability that both tests A and B are positive. I would then set up the problem like this: P(A|B)=(P(B|A)*P(A))/P(B), except that you can't figure out what P(B|A) is. Maybe I am making this too hard, but this is really stumping me.