Probability of getting a duplicate value when calling GetHashCode() on strings

Question

I want to know the probability of getting duplicate values when calling the GetHashCode() method on string instances. For instance, according to th

Answer 1

Just in case your question is meant to be what is the probability of a collision in a group of strings,

For n available slots and m occupying items:
Prob. of no collision on first insertion is 1.
Prob. of no collision on 2nd insertion is ( n - 1 ) / n
Prob. of no collision on 3rd insertion is ( n - 2 ) / n
Prob. of no collision on mth insertion is ( n - ( m - 1 ) ) / n

The probability of no collision after m insertions is the product of the above values: (n - 1)!/((n - m)! * n^(m - 1)).

which simplifies to ( n choose k ) / ( n^m ).

And everybody is right, you can't assume 0 collisions, so, saying the probability is "low" may be true but doesn't allow you to assume that there will be no collisions. If you're looking at a hashtable, I think the standard is you begin to have trouble with significant collisions when you're hashtable is about 2/3rds full.