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Are you ill? (Posted on 2005-01-03) Difficulty: 3 of 5
Suppose an illness that can affect 1% of the people. Also assume that there is a test for that illness, that gives the correct result 99% of the times.

If you take that test, and receive a POSITIVE result, should you worry much?

If you take it again, and once more get a POSITIVE, should you worry then?

How many consecutive POSITIVEs would you have to get in order to be sure that the chances of a wrong diagnostic are 1 in a million?

See The Solution Submitted by e.g.    
Rating: 3.7500 (4 votes)

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re(2): solution | Comment 8 of 18 |
(In reply to re: solution by Penny)

Not to worry, Penny, your record remains unblemished.  As Eric pointed out, Charlie is correct that after one positive test, the probability that you have the disease is 50%.
Positive means "the test shows you have the disease"

There are two ways the test could be positive:
(A): The test was accurate and you have the disease
(B): The test was wrong and you are disease free.

In each case the likelihood in the general population is .01*.99,  so Prob(A) = Prob(B) and therefore 50:50 that you have the disease.
But note that after zero tests, your probability of disease is 1%, and after one positive test it's up to 50%, so go ahead and worry a little (enough to get re-tested), just don't do a Ben Gazarra and make any life changing decisions.

(reference to TV show "Run For Your Life")
  Posted by Larry on 2005-01-03 20:37:44

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