So I'm trying to figure out the odds of winning a prize in a raffle where each person can buy multiple tickets but you can only win once.
My problem is the following:
- There are 2600 tickets sold
- There are 42 winning tickets drawn
- There is no limit on how many tickets you can buy
- I buy 10 tickets
- I know that there are only 600 people who have bought tickets (so all the tickets are distributed over the 600 people)
I have looked at booth of these threads:
Thread 1
Thread 2
and they helped me understand the problem well but I am still wondering if there is some way to calculate the probability better when you know how many people who have bought tickets. You still don't know how many tickets each person bought, but maybe you can calculate an average or something similar? I'm also thinking since the price of the tickets is 10$ each, it must be more unlikely someone bought 1000 tickets than say 1,5 or 10.
Any input or help is greatly appreciated!
*Edit:
All the prizes need to be distributed and if a person wins all the rest of their tickets become invalid. So they keep drawing until they have drawn 42 tickets which correspond to 42 unique individuals.
Best Answer
From what I understand of your problem, even if I buy all $2600$ tickets, I can get only one prize, i.e. although there are $42$ prizes, all needn't get distributed.
So we needn't bother about how many persons have bought how many tickets,
we can easily compute the $Pr$ that you win a prize.
You win a prize if all $42$ prizes don't fall in the $2590$ tickets not with you.
P(you win a prize) $= 1$ - P(you don't win a prize)
$= 1 - \dfrac{\binom{2590}{42}}{\binom{2600}{42}} \approx 0.1223$