In: Statistics and Probability
In a certain community, 4 percent of all adults over the age of 50 have tuberculosis (T.B.). A health service in this community correctly diagnoses 98 percent of all persons with T.B. as having the disease, and incorrectly diagnoses 3 percent of all persons without T.B. as having the disease. Find the probabilities that, a) the community health service will diagnose an adult over 50 as having T.B., b) a person over 50 diagnosed by the health service as having T.B. actually has the disease.