- #1

- 304

- 19

**This is not really a homework problem. This is something I enjoy thinking about.**

1. Homework Statement

1. Homework Statement

How many people should there be in a group to have a 50% chance of at least two of them having the same birthday.

I know that there a many pages explaining how to solve this and the answer itself. But I wanted to develop my own way to figure this out.

## Homework Equations

The problem boils down to how many unique pairs or handshakes can be formed in the group. That is N x (N-1) / 2 .

Also, the probability that a pair has the same birthday is 1/365.

Therefore, I think I have solve the following equation for N

N x (N-1) = 365

## The Attempt at a Solution

The approximate value of N is 20. For N=20, I think the probability of having at least one pair with the same birthday is 52%. But according this Wikipedia page there has to be 23 people for a 50% probability in this case.

Clearly I am doing something wrong. Maybe assigning the 1/365 probability to every pair is not correct. I don't know.