GATE | GATE 2017 MOCK II | Question 25

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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