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# False positive paradox

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.

If there is a medical test that is accurate 99% of the time about a disease that occurs in 1 out of 10,000 people, then testing one million people would approximately yield the following results:

Healthy and test indicates no disease (true negative)
$1,000,000 * \left(9999/10,000\right) * .99 = 989901$

Healthy and test indicates disease (false positive)
$1,000,000 * \left(9999/10,000\right) * .01 = 9999$

Unhealthy and test indicates disease (true positive)
$1,000,000 * \left(1/10,000\right) * .99 = 99$

Unhealthy and test indicates no disease (false negative)
$1,000,000 * \left(1/10,000\right) * .01 = 1$

If a patient received a positive response from the test the odds are ~99.02% (9999/10098) that they are healthy and the test is incorrect even though the test is 99% accurate.