How to calculate the odds of a collision in hash algorithms


Say I have a hash algorithm, and it's nice and smooth (The odds of any one hash value coming up are the same as any other value).

Now say that I know that the odds of picking 2 hashes and there being a collision are (For arguments sake) 50000:1.

Now say I pick 100 hashes. How do I calculate the odds of a collision within that set of 100 values, given the odds of a collision in a set of 2?

What is the general solution to this, so that I can come up with a number of hash attempts after which the odds fall below some acceptable threshold? E.g. I can say things like "A batch of 49999 hash value creations has a high chance of collision".

Best Solution