I hope this helps.....
1)What is the probability that the first slot of hash table will be empty?
=> 1st element has the probability of getting a slot is 1/k . not getting a slot is (k-1)/k
.: The probability that first slot being empty after n keys are hashed is (k-1)/k * (k-1)/k * (k-1)/k *.........n times = ((k-1)/k) ^ n
2) What is the expected number of slots that are being nonempty?
Ans: we can have k non empty slots,if keys go into the all slots of the table.
similarly we can have k-1,k-2,k-3,.....,1.
we can have any number from 1 to k-1 being non empty..