Note * This is what I have so far. I have answered A and B but am struggling wit

Question

Note * This is what I have so far. I have answered A and B but am struggling with C. Thanks for the help...

Suppose in a certain population, 11% of all adults over 50 have diabetes. If a community health service in this population correctly diagnoses 97% of all persons with diabetes as having the disease and incorrectly diagnoses 2% of all persons without diabetes as having the disease, find the probability thatL:

a)the community health service will diagnose an adult over 50 as having diabetes.

P(random adult > 50 will be diagnosed with Diabetes) = (.11 * .97) + (.02) * (.89) = .1245

b)a person over 50 diagnosed by the health service as having diabetes actually has the disease.

P(random Adult > 50 whose been diagnosed actually has Diabetes) = (.11 * .97) / .1245 = .857

c)a person over 50 diagnosed by the health service as not having diabetes actually does not havethe disease.

Explanation / Answer

c)probability of a person over 50 diagnosed by the health service as not having diabetes =1-0.1245 =0.8755

hence probability a person over 50 diagnosed by the health service as not having diabetes actually does not havethe disease =0.89*0.98/0.8755 =0.996231

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