What is the probability that at least one person in a room of $n$ people (excluding me) has the same birthday as I and that nobody else in the room shares a birthday on a different date? For practical purposes, pretend that leap years don't exist.
What is the probability that at least one person in a room of $n$ people (excluding me) has the same birthday as I and that nobody else in the room shares a birthday on a different date? For practical purposes, pretend that leap years don't exist.
As a follow-up, what is the expected number of people that have the same birthday as I in a room of $n$ people (excluding me) if nobody else in the room shares a birthday on a different day?