In a certain community, 8 percent of all adults over 50 have diabetes. If a health service in this community correctly diagnoses 95 percent of all persons with diabetes as having the disease And incorrectly diagnoses 2 percent of all persons without diabetes as having the disease, find the probabilities that
(a) The community health service will diagnose an adult over 50 as having diabetes;
(b) A person over 50 diagnosed by the health service as having diabetes actually has the disease.