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, nd 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.