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A clinic offers you a free test for a very rare, but hideous disease. The test they offer is very reliable. If you have the disease it has a 98% chance of giving a positive result, and if you don’t have the disease, it has only a 1% chance of giving a positive result. You decide to take the test, and find that you test positive. What is the probability that you have the disease?
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Marilyn Mahadeo
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Marilyn Mahadeo
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2 Solutions
 
d-glitchCommented:
Welcome to Experts Exchange.  I see this is your first question.

If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.

In this case, it looks like there isn't enough information to solve the problem.  If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
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d-glitchCommented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
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aburrCommented:
"In this case, it looks like there isn't enough information to solve the problem."
There is enough info to answer.
You have to combine two known probabilities.
If home work, show what you have done so far
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d-glitchCommented:
Without making some assumption about the meaning of very rare, you can not give a quantitative answer.

False positives will dominate until the disease prevalence exceeds 1% of the population.
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aburrCommented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.

False positives will dominate until the disease prevalence exceeds 1% of the population. "

d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
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In any case a lot of information about this type of problem can be found at the link
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
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d-glitchCommented:
As clear an explanation as possible.
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