It is estimated that approximately 8.12% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 94.5% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 2.5% 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").
It is estimated that approximately 8.12% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 94.5% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 2.5% of all adults over 40 without diabetes as having the disease.
a) Find the
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)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
