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)
10th Edition
ISBN:9780134753119
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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.

Transcribed Image Text:**Text for Educational Website:**
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It is estimated that approximately 8.14% of 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").
- Probability: **0.0321**
b) Find the probability that a randomly selected adult over 40 is diagnosed as not having diabetes.
- Probability: **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").
- Probability: **0.0003**
(Note: It will be helpful to first draw an appropriate tree diagram modeling the situation)
---
This text breaks down a statistical problem involving probabilities related to diabetes diagnoses. It explores concepts such as false positives and false negatives, which can be better understood through visual aids like tree diagrams that illustrate all possible outcomes and their probabilities.
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