I believe it's the other way around. If you inserted an item, then 'lookup(element)' is always true. However, you can get false positives, meaning that you migh

I believe it's the other way around. If you inserted an item, then 'lookup(element)' is always true. However, you can get false positives, meaning that you might also get true for items that have not been inserted. The probabilistic aspect is the false positive rate. One example of a use case would be a database keeping a set of existing column names in memory and testing a query against this set using a bloom/cuckoo filter before actually doing a disk read. That way, it doesn't have to do a disk read for a non-existent column or row.