It is estimated that approximately 8.12% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 94% of all adults over 4040 with diabetes as having the disease and incorrectly diagnoses 1.5% of all adults over 4040 without diabetes as having the disease.

a) Find the probability that a randomly selected adult over 4040 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 4040 is diagnosed as not having diabetes.

c) Find the probability that a randomly selected adult over 4040 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").

(Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)