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").
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").
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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I need help with C. Originally I got 0.00365 approx. But this answer is wrong.
![It is estimated that approximately 8.14% Americans are afflicted with diabetes. Suppose
that a certain diagnostic evaluation for diabetes will correctly diagnose 97% of all adults
over 40 with diabetes as having the disease and incorrectly diagnoses 3.5% 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").
0.0321
b) Find the probability that a randomly selected adult of 40 is diagnosed
diabetes.
having
0.8897
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18142083-b784-4318-a540-58b3c6d1a7fe%2Feaa0148c-fe3e-49c5-944d-69a78539ea8d%2Ffi0h1sk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:It is estimated that approximately 8.14% Americans are afflicted with diabetes. Suppose
that a certain diagnostic evaluation for diabetes will correctly diagnose 97% of all adults
over 40 with diabetes as having the disease and incorrectly diagnoses 3.5% 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").
0.0321
b) Find the probability that a randomly selected adult of 40 is diagnosed
diabetes.
having
0.8897
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)
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