Isn't the "classical" question usually, "For N people, what is the probability that at least 2 share the same birthday?"  I believe that is the solution to that is given by Marco.  But, the original question seemed to be exactly two people out of 100.  The "at least" probability would need to multiplied by the probability none of the other 98 share the same birthday as our lucky two.

So, let's try an approximation by brute force for exactly 2:

Playing with this a bit more: brute force probabilities that  for n people,  at most m share the same birthday:

The crossings at p=1/2 are interesting.....

:Thank you,

For how long it takes me for writing the mathematica without asking questions here, or help others?

Both pictures are very nice.

Dear Craig, 

I am not really sure about the original question either. You are absolutely right: In fact, I did read it as
"How to find the probability for (at least/any) two people who have the same birthday among the 100 people?"

Without any quantifier like "exactly" that is the default mathematical interpretation, I believe. Otherwise I would have expected the question to explicitely state "exactly two people".
Here is the usage I adhered to:
http://english.stackexchange.com/questions/36375/meaning-of-no-two

You are quite right that Michelle's question might have been about exactly two people. And as you say, the question you answer is"  ..., exactly two people out of 100."  which is a different question to the one I wanted to answer.

By the way, the question could technically also mean exactly two people share their birthdays and none of the remaining 98 people share their birthdays with anyone - so there is no other couple of people sharing the same birthday (which might be different from the first couples').

M.