http://qs1969.pair.com?node_id=145788


in reply to Birthday Chances

The question here is: What are the chances of any n people not having unique birthdays? That's a difficult question. But the cool thing about probability is that you can always find the probability of something by subtracting the probability of its inverse from one. So instead, ask: What are the chances of any n people having unique birthdays? That would be:

(1/365) * ( 1/365 -1) * (1 /365 -2 ) * ... ( 1/365 - (n-1))

And once you have that, the answer to the original question is:

1 - ( (1/365) * ( 1/365 - 1 ) * ( 1/365 - 2) * ... ( 1/365 - (n-1)))

Now just plug in different values of n to find the odds of n people not having unique birthdays.