Bloom Filter ?

1. “Whenever a list or set is used, and space is consideration, a Bloom filter should be considered. When using a Bloom filter, consider the potential effects of false positives.” S is a set of n elements. Set of k hash functions with range {1...m} (or {0...m − 1}).

Mathematically
  If m is the number of bits in the array, the probability that a certain bit is not set to 1 by a certain hash function during the insertion of an element is

If k is the number of hash functions, the probability that the bit is not set to 1 by any of the hash functions is