Suppose there's a lottery. Each ticket sold has probability $p$ of winning, and they are all independent of each other. The size of the jackpot is $j$. If there are $n$ winners, each winner gets a payoff of $j/n$ dollars. The total number of tickets sold is $t$.
What is the expected value of a lottery ticket? Also, given that I win, what is the probability that I have to share the jackpot with at least one other person?
PS - I think I know the answer, but have failed to convince someone else, so I'm looking for a third-party to give an answer.