It is estimated that approximately 8.13% Americans are afflicted with diabetes. Suppose that a certain diagnostic...

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It is estimated that approximately 8.13% 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"). (Note: it will be helpful to first draw an appropriate tree diagram modeling the situation) 1 diabetes\diagnosis positive (+) negative (-) Total 2 Yes (Y) 3 No (N) 4 Total A Bayes Thm problem. You must either use a contingency table or a tree Write down the desired conditional probability and its formula when appropriate. 3456788 9 It is estimated that approximately 8.13% 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"). (Note: it will be helpful to first draw an appropriate tree diagram modeling the situation) 1 diabetes\diagnosis positive (+) negative (-) Total 2 Yes (Y) 3 No (N) 4 Total A Bayes Thm problem. You must either use a contingency table or a tree Write down the desired conditional probability and its formula when appropriate. 3456788 9