# Birthday buddies

Computer Science Level 2

For each integer $$n\geq 1$$, let $$p(n)$$ denote the probability that, in a room with $$n$$ people chosen at random, two (or more) of them share a birthday. Find the value of $$n$$ for which $$p(n)$$ is as close as possible to $$\frac{1}{2}.$$

Details and assumptions

Every year has 365 days, a person's birthday is equally likely to fall on any of the possible 365 dates, and the birthdays of different people are independent of each other.

×