A new medical test has been developed by a major pharmaceutical manufacturer for detecting the incidence of a bacterial infection. Of the people who actually have the disease, the test will correctly indicate that the disease is present 95 percent of the time. Among people who do not have the disease, the test incorrectly indicates the disease is present 5 percent of the time. The health department of a major east coast city is contemplating making the test available to a population in which .2 percent of the individuals in the population actually have the disease.

a. For a randomly selected individual from the population, if the test indicates that the person has the disease, what is the probability that the person actually does have the disease?

b. For a randomly selected individual from the population, if the test indicates that the person does not have the disease, what is the probability that the person actually does not have the disease?