Question

Find the chance of a "match": that is, at least two people in the room have the same birthday.

Answer 1

look up "birthday problem' in wikipedia... shows you the whole theory on this topic

Answer 2

n p(n)
10 11.7%
20 41.1%
23 50.7%
30 70.6%
50 97.0%
57 99.0%
100 99.99997%
200 99.9999999999999999999999999998%
300 (100 − (6×10−80))%
350 (100 − (3×10−129))%
365 (100 − (1.45×10−155))%
366 100%