There are $n$ participants in the lottery and if 1 wins the prize of $M$ USD is divided equally between the participants.
Each participant picks a number from $\{1,\dots,N\}$ randomly (two can pick the same number). The winning number is picked randomly from $\{1,\dots,N\}$.
Admond is one of the participants. Let $A$ be the profit of Admond.
Given that it doesn't cost money to participate in the lottery. What is the expected value $\mathbb{E}(A)$?
Please help me approach this one.