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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?

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  1. (97 × 97 × 97) / 1003
  2. (99 × 98 × 97) / 1003
  3. (97 × 96 × 95) / 1003
  4. (97 × 96 × 95) / (3! × 1003)

Answer (Detailed Solution Below)

Option 1 : (97 × 97 × 97) / 1003
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Detailed Solution

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Chaining:

  • Each slot may contain a chain of elements but in linear probing, we can insert only one element in every slot.

 

  • In order to insert element 1, we have 4 to 100 = 97 slots out of 100 slots
  • In order to insert second element, we have 4 to 100 = 97 slots out of 100 slots
  • In order to insert third element, we have 4 to 100 = 97 slots out of 100 slots
  • Required probability 


Hence option 1 is the correct option.

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