Final answer:
To calculate the probability that the first 3 slots are unfilled after the first 3 insertions in a hash table with 100 slots using chaining and assuming simple uniform hashing, we need to determine the probability that each of the first 3 insertions goes into one of the remaining unfilled slots. The probability is approximately 0.0941094. The correct answer is option A. (97 x 97 x 97)/1000000
Step-by-step explanation:
To calculate the probability that the first 3 slots are unfilled after the first 3 insertions in a hash table with 100 slots using chaining and assuming simple uniform hashing, we need to determine the probability that each of the first 3 insertions goes into one of the remaining unfilled slots. Since collisions are resolved using chaining, we can assume that each insertion will go into a different slot as long as the previous slots are already filled.
After the first insertion, there are 100 slots available and 1 filled slot. So, the probability that the second insertion goes into an unfilled slot is 99/100. After the second insertion, there are 2 filled slots and 98 unfilled slots available, so the probability that the third insertion goes into an unfilled slot is 98/100.
Therefore, the probability that the first 3 slots are unfilled after the first 3 insertions is (99/100) x (98/100) x (97/100) = 0.941094 or approximately 0.0941094.