# At least two people in a group of 23 have the same B-Day ...

including year? …

Always wondered what the odds would be if the birth year was included? How large a group would be required for even odds if the birth year was included in the criterion?

It depends what the allowable range of years is. With one year, there are 365 possible slots, and the odds work out such that the threshold is 23. With two years, there are 730 days, and the odds change. So, how many years are you talking about? If everybody in the room is within 10 years of each other, you get one answer. If 100, another. If you include Julius Ceaser or Neandrathal man, things change.

Another way of looking at it: Imagine a game where 4 people guess a number between 1 and 5. Odds are good of at least two of them picking the same number, right? Now, instead of limiting the choices, say they can pick any positive integer up to 5000. What are the odds? What if it’s 10,000? What if it’s any number at all? What if it’s any positivie integer up to some number, but you don’t know what that number is?

You have to make some sort of assumption about the age distribution of the people. Assuming that they are less that 100 years old, and that the ages are randomly distributed between 0 years and 100 years, I just calculated that with 226 people there is slightly more than a 50% chance of 2 having the same birthday.