Question

In a certain community, 10% of all people above 50 years of age have diabetes. A
health service in this community correctly diagnoses 95% of all persons with
diabetes as having the disease, and incorrectly diagnoses 5% of all persons without
diabetes as having the disease. Find the probability that a person randomly selected
from among all people of age above 50 and diagnosed by the health service as having
diabetes actually has the disease.