There's an old Bayesian thought exercise: Imagine that the test for Condition X has a 1/100 false positive rate (specificity), but X occurs in only 1/1000 peopl

There's an old Bayesian thought exercise: Imagine that the test for Condition X has a 1/100 false positive rate (specificity), but X occurs in only 1/1000 people. If you select a random person and they test positive for X, it's more likely that they hit the 1% false positive than that they actually have X. (This comes up all the time in practice). So if you have a database of 10,000 people and 1.1% false positive rate, you're likely to get several false positives. Unless you stop searching as soon as you find a positive, of course...