Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?
(A)
(97 × 97 × 97)/1003
(B)
(99 × 98 × 97)/1003
(C)
(97 × 96 × 95)/1003
(D)
(97 × 96 × 95)/(3! × 1003)
Answer: (A)
Explanation:
Simple Uniform hashing function is a hypothetical hashing function that evenly distributes items into the slots of a hash table. Moreover, each item to be hashed has an equal probability of being placed into a slot, regardless of the other elements already placed.
Probability that the first 3 slots are unfilled after the first 3 insertions = (probability that first item doesn\'t go in any of the first 3 slots)* (probability that second item doesn\'t go in any of the first 3 slots)* (probability that third item doesn\'t go in any of the first 3 slots) = (97/100) * (97/100) * (97/100)
Quiz of this Question
Please comment below if you find anything wrong in the above post