Question

Consider a hash table with n buckets, where external (overflow) chaining is used to resolve collisions. The hash function is such that the probability that a key value is hashed to a particular bucket is 1/n. The hash table is initially empty and k distinct values are inserted in the table. What is the probability that bucket number 1 is empty after the K insertions?
What is the probability that no collision has occurred in any of the K insertions?
What is the probability that first collision occurs at the Kth insertion?

Answer 1

probability that the hash fun mapping a key to a bucket number 1= 1/n and probability that the hash fun not mapping a key to a bucket number 1= 1-(1/n)
probability that the bucket no. 1 is empty=none of these k keys mapped to bucket no. 1 =(n-1/n) (n-1/n) (n-1/n)...k times =(n-1/n)^k