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 please steps by steps !. Created by Ian Chen. en - en

the probabilities ：(a) the community health service will diagnose an adult over 50 as having diabetes8% *95% + ( 100% -8% ) *2% = 9.44 %=0.0944(b) a person over 50 diagnosed by the health service as having diabetes actually has the disease 8% *95%/0.0944=0.076/0.0944=95/118