Question
Iin a certain community, 8% of all adults over 50 havediabetes. if a health centre in this community correctly diagnoses95% of all persons with diabetes as having the disease, andincorrectly diagnoses 2% of all persons without diabetes as havingthe disease, find the probability that: a) The community health centre will diagnose an adult over 50as having diabetes. b) A person over 50 diagnosed by the health centre as havingthe disease actually has the disease. Iin a certain community, 8% of all adults over 50 havediabetes. if a health centre in this community correctly diagnoses95% of all persons with diabetes as having the disease, andincorrectly diagnoses 2% of all persons without diabetes as havingthe disease, find the probability that: a) The community health centre will diagnose an adult over 50as having diabetes. b) A person over 50 diagnosed by the health centre as havingthe disease actually has the disease.
Explanation / Answer
First, make a Baye's rule stem like this: Hasdiabetes Doesn't Have Diabetes 8% 92% CorrectlyDiagnosed FalseNegative FalsePositive CorrectlyDiagnosed 95%*8% 5%*8% 2% *92% 98%*92% 7.6% .4% 1.84% 90.16% Part a) add Correctly diagnosed as havingdiabetes with the false positive (7.6%+1.84%)=9.44% Part b) Divide the proportion correctly diagnosed as havigndiabetes from the total proportion diagnosed (7.6%/9.44%)=.8051, orabout 80.5% Part b) Divide the proportion correctly diagnosed as havigndiabetes from the total proportion diagnosed (7.6%/9.44%)=.8051, orabout 80.5%