Planning a fundraiser single game.... need help with statistics PLEASE!!!

Planning a Bonanza style bingo fundraiser (sort-of), but need statistics -- please help!
- I have 3000 1on cards (given to me for free) and I want to use them to raise money
- I plan on pre-drawing 20 to 25 bingo numbers (depending on your advice) and selling the cards after the numbers are drawn
- I plan on using them at an event that annually brings approx. 400 people (but I know not everyone will buy a card)

What I need to figure out is;
- How many cards do I need to sell at & what price to make a profit for my non-profit organization
- How many bingo numbers I should pre-draw (20-25?)
- How many cards will get a straight line bingo in how many cards sold, which will indicate how much I should offer as a prize.

I know that there are A LOT of variables in this question, so I know that the answer will not be precise... I just don't want to loose money over-all.

Any info you can give would be greatly appreciated!!!

Maybe somebody with more time on his hands will help, but I think this is the kind of thing you should be paying to get an answer for.

These numbers seem a bit low, but I ran 20 million games on a single card to see how many balls it would take for that card to get a 5-in-line (with center space free) Bingo:

Balls	Bingo Prob
10	1 / 1232.058
11	1 / 767.165
12	1 / 502.361
13	1 / 340.038
14	1 / 237.02
15	1 / 170.478
16	1 / 125.404
17	1 / 93.93
18	1 / 71.62
19	1 / 55.525
20	1 / 43.718
21	1 / 34.82
22	1 / 28.081
23	1 / 22.87
24	1 / 18.823
25	1 / 15.632

Note that each number is for that many balls or fewer

Also remember that this is for just one card

That's awesome!!!! So if I understand; if I called 21 numbers then 1 in every 35 cards would get a bingo?

Quote: JuanitaKelly214

That's awesome!!!! So if I understand; if I called 21 numbers then 1 in every 35 cards would get a bingo?

Well, sort of - but you have to remember that it's "1 in 35 cards" if you call 21 numbers even if somebody has a bingo in 20 or fewer.

I assume that, if there is a tie, any prize is split, or there's some sort of drawing for it, so you're only really interested in whether or not anybdy gets a bingo - not necessarily how many.

If there are 100 cards in a game, the probability that nobody gets a bingo in 21 numbers is (1 - 1/34.82)¹⁰⁰ = about 1 / 18.43.

Actually I plan to use the bingo cards as a sort of form of lottery. The numbers on their card are the numbers they are playing in the lottery.... the numbers I pre-call are the actual lottery numbers... the player has to be able to cover 5 numbers in a row (or 4 with the free space) in order to win a prize, so I need to know how many of those cards will win a prize so I can determine how much I need to charge for each card in order to make money for my non-profit. SO if I know that 1 in every 35 cards will statistically get a bingo, then I know that I need to make the cost per card more than the payout for 3 in every 100 cards. At least that's what I'm guessing.