A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population tests positive, what is the conditional probability that the person does, in fact, have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test reliable?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A diagnostic test for a certain disease has 95% sensitivity and 95% specificity. Only 1% of the
population has the disease in question. If the diagnostic test reports that a person chosen at random
from the population tests positive, what is the conditional probability that the person does, in fact,
have the disease? Are you surprised by the size of the answer? Do you consider this diagnostic test
reliable?

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