If you have a set of numbers D = {x1, x2, x3, ..., xn}, you can determine if there is any repeated numbers in D using an algorithm using a direct access table (hashing).

But how do you determine a probability space when deriving the expected running time?

For the probability space, are we basically saying what is the probability that a number in D is repeated, but how do you get a probability from this?

Can anyone help please?

I am thinking, that for each number xi in D, you have to check if it is the same number as all the other ones in D, so there is n-1 other numbers in D.