membership structures another equally effective way of generating independent hashing functions is to append some known value to the end of each item before it is hashed for instancea might be appended to the item before hashing it to get the first hash function could be appended to the item before hashing to get the second hash function likewisea might be appended to get the third hash function value so looking up rabbit in the bloom filter is accomplished by first hashing rabbit rabbit and rabbit with the same hashing function since the hashing function is uniformly distributedthe values returned by the three hashed values will be independent of each other andall items with appended will themselves be uniformly distributed likewise for items with appended and with appended the bloom filter size it is possible to find the required bloom filter size given number of items to insert and desired false positive probability the probability of any one location within bloom filter not being set by hash function while inserting an item is given by the following formula where the filter consists of bits if the bloom filter uses hash functionsthen the probability that bit in the bit array is not set by any of the hash functions required for inserting an item is given by this formula if items are inserted into the bloom filter then raising this formula to will provide the probability that bit within the bloom filter' bit array is still zero after inserting all items so we have nk sothe probability that bit in the bloom filter is after inserting items while using hashing functions is given by this formula nk now consider looking up an item that was not added to the bloom filter the probability that it will report false positive can be found by computing the likelihood that each location within the bloom filter is for all hashing functions this is expressed as follows  nk this formula contains sequence that can be approximated using the natural log [ as  ekn/ this copy belongs to 'acha