A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population test positive, what is the conditional probability that the person does, in fact, have the disease?

Lets agree on some notation.

S = population with disease so

D = has disease

+ = test positive

I estimated a and b, but I am not sure if there is a way to do it without arbitrary estimation.