1. The problem statement, all variables and given/known data The test for an illness is 90% accurate (meaning it gives a positive result 90% of the time if the patient has gingivitis and a negative reading 90% of the time if the patient doesn't). 4% of all people have this illness. a) calculate the probability the test will be positive for a random patient b) once the patient tests positive, what is the probability that he actually has the illness? 2. Relevant equations 3. The attempt at a solution a. P(positive): b. P(has disease given test is positive): I'm completely lost. For a, I would think that the chances of the patient being actually ill are 0.04 and then him test positive is .9 of that, sooo the answer would be 0.036, but I have no idea how to make that look like an actual probability problem or if the answer is even correct... For b, I don't even know where to start. If someone could point me in the right direction, I would be much obliged. Thanks!