> = P[ mal ] / P[ pos ] ~= 1.0 You didn't prove this. You can't swap subtraction for multiplication. It's not equivalent to > [ pos ] - P[ mal ] ~= 0 1e-10

> = P[ mal ] / P[ pos ] ~= 1.0 You didn't prove this. You can't swap subtraction for multiplication. It's not equivalent to > [ pos ] - P[ mal ] ~= 0 1e-100 - 1e-200 ~= 0, but 1e-200 / 1e-100 = 1e-100 That's the point of the base rate fallacy. https://en.m.wikipedia.org/wiki/Base_rate_fallacy https://en.m.wikipedia.org/wiki/Base_rate_fallacy False negative rate doesn't matter. A low false positive rate can be much larger than the true positive rate. Imagine an extremely rare toxin that always turns your skin blue. Only 100 people in the world have it. But 1000 people are wearing blue face paint at any given time. A diagnostic test "are you blue?" Would have no false negatives and very low false positives for the toxin, just like a Bloom filter. But a positive test would not mean highly likely to have the toxin; it would mean highly likely to be wearing face paint.