Using the calculations on https://hur.st/bloomfilter/?n=50&p=&m=1000&k= I can see that there is a 1 in 14,895 chance of a collision between one of these fifty entries and a random value (when using just 1,000 bits of storage). Assume elements are UUIDs.
How does this probability change, if the 50 elements are 50 from a set of 100, and we only care about false positives within that set of one hundred?
(If that 100 was an unchangeable well-known indexed set, we could just use 100 bits and XOR and ignore Bloom Filters. Unfortunately this set might sometimes be 102 or 105 elements, and one side might know about only 95 or 103 of them.)