Suppose there is a medical diagnostic test for a disease. The sensitivity of the

test is .95. This means that if a person has the disease, the probability that the

test gives a positive response is .95. The specificity of the test is .90. This

means that if a person does not have the disease, the probability that the test

gives a negative response is .90, or that the false positive rate of the test is .10.

In the population, 1% of the people have the disease.

What is the probability that a person tested has the disease, given the results of the test is positive? Let

D be the event "the person has the disease" and let T be the event "the test

gives a positive result."

Any help would be much appreciated.