I think it's answer is (A) that is after insertion of 5 keys, the insertion of new key will exceed 0.5...
and (10) not be the answer.. even if I think in that way that insert 10 keys.. then we have 10 slots vacat.. probability of collision = 10 / 20 = 0.5.. He used the word "exceed".. exceed means greater than.. It doesn't mean "greater and equal", but it is equal.. !!
explaination:
probability of inserting a new key is not independent they depends on previous insertions. So basically it is a conditional probability.. p("insetion of new key" | "insertion of m keys")
We are asking to insert the new key with probablity exceeds 0.5
0.5 < probabiltity of collision when (m + 1) keys are inserted!!
=> 0.5 < 1 - p(all are hashed to a different location)
after insertion of 5 keys
p(all are...) = 1 * 19/20 * 18/20 * 17/18 * 16/20 = 0.581 => 1 - 0.581 = 0.418 < 0.5..
after insertion of 6 th keys
it exeedes 0.5..
so, after hashing of 5 keys new key hashsed collides with an existing one exceed 0.5..
So.. (A) is the answer...