Image via Wikipedia

While our country celebrates its birthday today, here’s an interesting problem from the field of mathematics.  I first learned of the Birthday Problem in a statistics class I took at NYU (at least I remembered something, Professor Melnick).

In summary, the Birthday Problem calculates the probability that at least two people from a randomly chosen group share a birthday. 

At the extremes this is easy to understand.  Excluding leap year, there are 365 potential birthdays.  If you have a randomly chosen group of 366, it follows that the probability is 100% that at least two people share a birthday.  The outcome is absolutely assured.  Conversely, if two people meet in the street, and compare their birthdays, if is very unlikely that they will be the same.

What makes the Problem particularly interesting is how small a group you need to assemble to make the probability higher than 50%.

Without reseaching the answer (you are on the honor code), how large would you expect the group to have to be to make the probability 50%?  How about 95%?  The answers may surprise you…