[Edgewaterbaby]

This is not a Homework question. It is a real scenario that I need to resolve. I guess I want it to be fair. My son goes to Catholic School (Queen of Angels in Chicago). I was required to buy 70 raffle tickets at $5 a ticket. Total $350.

The ticket explains this:
1. Once a week on Friday, a raffle ticket will be drawn to determine
The winner for that week. The raffle ticket is returned to the pool
For the next week's drawing.
2. The weeks for which the winning raffle tickets will cover will run
From Oct 8, 2010 to last Friday of May 2011.
3. All Completed raffle tickets must be returned Nov 30. (They will go back and draw previous winners from Oct 8th to Nov 30th)

Prize:
34 weekly winners at $150
2 Special draws for Christmas 2010 and Easter 2011 with winner gets $500

My problem: It is 1/28/11. I missed almost half of the drawings. I either want
(1) Some money back? How much back? Half?
Or
(2) More raffle tickets to increase odds of winning. I missed half the draws.

No ideas the total number of tickets. It seems like it could change since 2/1/11 they are willing to start including my tickets in a draw.

Thanks!! Help, please.

[Edgewaterbaby]

So after speaking to my great uncle, a master probability expert, I got an intuitive answer. Raffles are a losing proposition. The non-profit has the winning odds. My first priority get as much cash back as possible. If that is not possible than try to get as many additional tickets as possible. Okay duh. He said there is no way to calculate how many tixs I should ask for.

[galactus]

I would say he is correct. Without knowing how many tckets were sold it is difficult to find the probability of winning and the expected cost of each ticket.

[Unknown008]

Well, if it is confirmed that there is a minimum ticket each student should bring, we can get an estimate by knowing the number of students in a class, and the number of classes in the school.

But my guess is that the number of tickets will be a very large number compared to 70 tickets :p

[jcaron2]

You don't need to know how many tickets were sold; you only need to know the relative value of each of your tickets compared to a normal (full-year) one.

There are 34 drawings for $150 each (for a total of $5100 in prize money), plus an additional $500 each for the two holidays, for a grand total of $6100 dollars.

Assuming you were in today's drawing, that means your tickets have a chance to win in 18 of the drawings, plus Easter, so each of your tickets only has a chance at $3200, whereas the rest of the tickets have a shot at $6100.

That means each of your tickets is only worth 32/61 as much as a normal one (or about $2.62 apiece). Therefore, you should either get 29/61 of your money back ($166.39), or you should get 61/32 times as many tickets (or about 133 total - a few more now, since you only had 70 in today's drawing).

That being said, there's another angle to consider here: Clearly, as your great uncle pointed out, this is a money-making venture for the school. Any one person's chances of winning are rather small, so really this is just a way of extracting extra money out of the students' parents. If you averaged it out for all of the students in the school, the tickets probably end up costing the parents something like $4.75 apiece, because there's a small chance that a ticket will pay off. Of course, in reality the cost was the full $5 for most people, with a few (no more than 36 people) effectively paying significantly less (or even getting money back). But like I said, on average the tickets probably end up netting the school something well north of $4 apiece. So the question then becomes, did the school prorate the number of tickets they forced you to buy to reflect the shortened school year? In other words, if they made everybody else buy 150 tickets per child back in November, but you only had to buy 70, then I'd argue that charging you the full $5 apiece is perfectly fair. But if all of the parents only had to buy 70 tickets per child way back at the beginning, then I'd demand and extra 65 tickets or so, or a $166 refund!

Either way, best of luck in the drawings!