Ah this is quite interesting, an excerpt from Fooled By Randomness by Nassim Nicholas Taleb, page 159:
The Birthday Paradox
The most intuitive way to describe the data mining problem to a non-statistician is through what is called teh birthday paradox, though it is not really a paradox, simply a perceptional oddity. If you meet someone randomly, there is a one in 365.25 chance of you sharing their birthday, and a considerably smaller one of having the exact birthday of the same year. So, sharing the same birthday would be coincidental event that you would discuss at the dinner table. Now let us look at a situation where there are 23 people in a room. What is the chance of there being 2 people with the same birthday? About 50%. For we are not specifying which people need to share a birthday; any pair works.
Now 50% is really high chance! Bet you never thought of that. Well, you could read more at Wikipedia for the exact math of The Birthday Problem or the Birthday Attack.