It is estimated that approximately 8.23% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 98% of all adults over with diabetes as having the disease and incorrectly diagnoses 3.5% of all adults over without diabetes as having the disease.

a) Find the probability that a randomly selected adult over does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called "false positives").
b) Find the probability that a randomly selected adult of is diagnosed as not having diabetes.
c) Find the probability that a randomly selected adult over actually has diabetes, given that he/she is diagnosed as not having diabetes