Fogbow

Since there are two birthdays this week in my family it made me think of this math problem that I read about a long time ago. It goes like this:

How large a group of people do you need before there is a better than even chance that two people in the group will have the same birthday (month and day)? I am ignoring people born on February 29th for simplicity.

Can you solve it or get close without resorting to Google or the Internet?

IIRC the formula is (364/365) * (363/365) * (362/365) * ... * ((365-n)/365)
and the answer becomes < 50% at n = 23

You can approximate it as 1.2 * sqrt(365)

Close, the generic term is (366-n)/365 (because with n=1, there's a 100% chance that nobody shares a birthday since there is only one birthday)

From WIkipedia:
https://en.wikipedia.org/wiki/Birthday_problem

Yes, the correct answer to my question is 23. At a group size of 23 the probability that two people have the same birthday crosses 50% to 50.7%. For the average school class size of about 30 it is over 70%. It grows quickly as can be seen in this table and graph: