Ask "have I seen this before?" — using a tiny fixed array of bits, and none of the items themselves.
A Bloom filter never gives a false negative: "not present" is always the truth. It only ever errs the other way — a confident "present" that's wrong. You trade a little certainty for enormous space savings, and the price is a number you can dial and check, not hope about. The measured rate above should sit close to — and usually a hair above — the formula, because the classic formula is a known slight under-estimate. Even the theory wants verifying.