400 people are in a room. What is the probability of two random people having the same birthday?

4.6k Views Asked by At

There are 400 people in a room. I pick two people at random. What is the probability that they have the same birthday?

I know that there must be two people in the room who share the same birthday through pigeonhole principle.

But if I pick two people at random I am not sure how to calculate the probability.

1

There are 1 best solutions below

2
On

The way the problem is stated, the number of people in the room is irrelevant. The probability that any two people have the same birthday is approximately $\frac{1}{365.25}$ assuming a uniform distribution of birthdays over time.