Given a hash table with n keys and m slots with simple uniform hashing. If collisions are resolved by chaining then what is the probability that the first slot ends up empty ?
(A) (1 / m)n
(B) [1 – (1/m)]n
(C) (1/n)m
(D) [1 – (1/n)]m
Answer: (B)
Explanation: Probability of one particular slot = 1/m ( because total m slots)
Probability that a value should not go in one particular slot = 1 – (1/m)
For n values (keys) probability = [1 – (1/m)]n
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