Testbook Test Series: Programming & DS - Hashing

Question

The keys 44, 63, 29, 78, 23, 6, 81, 14, 13, 12 and 52 are inserted into an initially empty hash table of length 12 using linear probing with hash function h(k)= k mod 12. What is the probability that the 10th slot will be filled next?

i. 11/12

ii. 1/12

iii. 10/12

iv. 1

The answer given is i but according to me it should be iv because after we insert all the given numbers in the hash table only one slot  is left which have a probability of filling as 1 because no matter what index we get for the next insert we are going to fill 10th slot only.

Comments

If 9th and 10th both are empty then filling 10 th  will have 11/12 probability ?

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If 9th and 10th are empty them the probability of filling 10th will be 1/12 because 10th gets filled only when element is directly mapped to it, otherwise 9th will get filled, therefore the probability of filling 9th will become 11/12.

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answer will be 1 only, it's a sure event, there is only 1 bucket left empty.