It is estimated that approximately 8.46% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 4% of all adults over 40 without diabetes as having the disease.

a) Find the probability that a randomly selected adult over 40 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 40 is diagnosed as not having diabetes.

c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").