A test for a disease is such that it correctly detects the disease in 88% of the individuals who actually have the disease (i.e P(T|D) = 0.88). Also, if a person does not have the disease, the test will report that he or she does not have it with probability 81% (i.e P(T| D) = 0.81).

Suppose this test is used to screen for the disease in the general population where only 1% of the population has the disease in question (P(D) = 0.01).

a. what proportion of this general population will test positive for the disease (i.e what is P(T)?)

b. if a randomly - selected individual tests positive for the disease, what is the conditional probability that she does, in fact, have the disease(i.e what is P(D|T))?