SOLUTION: Suppose that 4% of all adults over 40 have diabetes. A certain physician correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that 4% of all adults over 40 have diabetes. A certain physician correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses      Log On


   

Question 356122: Suppose that 4% of all adults over 40 have diabetes. A certain physician correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3% of all adults over 40 without diabetes as having the
disease.
8) Draw a tree diagram and label it with appropriate probabilities.
9) Find the probability that a randomly-selected adult over 40 is diagnosed as not having diabetes.
10) Find the probability that a randomly-selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I rounded all calculations to 3 decimal places.
.95*.04=.038 of population correctly diagnosed as diabetic.
.03*.96=.029 of pop. incorrectly diagnosed as diabetic.
.
9)
1-.038-.029=.933 probability that a randomly-selected adult over 40 is diagnosed as not having diabetes by this physician.
.
10)
.002/(.931+.002)=.002/.933=.002 probability that a randomly-selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes.
.
Ed