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.
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.