Question 1165956: It is estimated that approximately 8.43% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 98% 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").
(Note: it will be helpful to first draw an appropriate tree diagram modeling the situation)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Look at 10000 people
843 have diabetes
======Test+======Test-=====Total
DM --- 826.14---- 16.86 ----- 843 The 98% is applied to here for test +
Not DM=228.92===8928.08 ====9157 The 97.5 is applied here for test- (or 2.5% for test +)
Total --1055.06 8944.94. 10000
a.False positive is 228.92/1055.06=21.7%
b. That is 91.57%
c. Diagnosed as not having is 8944.94 and actually having it is 16.86, so the probability is 16.86/8944.94, or 0.00195 or 0.2%
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