

Suppose you undergo a medical test for a relatively rare disease. Your doctor tells you that, according to surveys by medical statisticians, the disease has an incidence of 1% among the general population. Thus, before you take the test, and in the absence of any other evidence, your best estimate of your likelihood of having the disease is 1 in 100, i.e. a probability of 0.01. Then you take the test. Extensive trials have shown that the reliability of the test is 79%. More precisely, although the test does not fail to detect the disease when it is present, it gives a positive result in 21% of the cases where no disease is present  what is known as a "false positive." When you are tested, the test produces a positive diagnosis. Given the result of the test, what is the probability that you actually have the disease?

This page was last changed on February 17, 2008 