False positive paradox

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The false positive paradox is a situation where the incidence of a condition is lower than the false positive rate of a test and therefore when the test shows that a condition exists, it is probable that the result is a false positive.

For example, if there is a medical test that is accurate 95% of the time about a disease that occurs in 1 out of 10,000 people, then if you tested all 10,000 people you would yield false positives for 499 people and one true positive for the person that had the disease. Thus, if a patient received a positive response from the test the odds are 99.8% (499/500) that they do not have the disease even though the test is 95% accurate.