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?
(In reply to re: solution
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