Here is how a lottery works: There are 30'000 participants. Out of all of them, 1 wins 100\$, 10 win 10\$, 100 win 1\$, and 1'000 win 0.1\$. For each run of the lottery, a participant can only win once.
$X$ is the total amount won by a participant after $n$ tries. I have absolutely no clue on how to find $n$ such that $E(X \ge x) = 0.5$, with $x$ a constant, say for instance $x = 100$
My knowledge of probabilistics is nowhere to be found, and it is trivial to say that this is none of the classical probability laws. The only thing I can do is an approximation of the result using a binomial law for each payout and summing the probabilities. But it sucks.
Thanks for your help!