19. Suppose you are tested to see if you have a rare disease. Assume that if you have the disease, your testwill always come back positive, but if you do nothave the disease, there is still a 0.001 chance that youwill test positive. In reality, only 1 of 10,000 peoplehave the disease. Your doctor calls and says that youhave tested positive. He is sorry but there is a 99.9%(120.001) chance that you have the disease. Is hecorrect? What is the actual probability that you havethe disease?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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19. Suppose you are tested to see if you have a rare disease. Assume that if you have the disease, your test
will always come back positive, but if you do not
have the disease, there is still a 0.001 chance that you
will test positive. In reality, only 1 of 10,000 people
have the disease. Your doctor calls and says that you
have tested positive. He is sorry but there is a 99.9%
(120.001) chance that you have the disease. Is he
correct? What is the actual probability that you have
the disease?

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