Consider a test for disease that has 99% sensitivity and 98% specificity. The null hypothesis D_0 is that the person does not have the disease. Assume a prevalence of D_0 = 99.5% and that only 0.05% of people don't have the disease.

Find:

a) the probability that the individual test positive given D_0 (they don't have disease)

b) the probability they don't have the disease given they test positive

c) the probability of testing positive a second time given they test positive once. It is safe to assume that the two tests are independent given the disease status. eg. P(first test positive and second test positive) = P(first + | C) P(2nd + | C)