Maths help please

[Pushmepullu]

Help!!!

I’ve been asked to run the bottle tombola at a school fete next weekend. I’ve been left to work out the odds based on 80 bottles, selling the tickets at 3 for £1. This stall is the biggest money maker for them. Problem is I can’t work out how many raffle tickets I need to fold! Ticket numbers 5 and 0 are winning tickets.

Can anyone offer any advice or do the sums for me please?

The person that normally runs it is ill and I can’t ask her how to do this.

Do you mean numbers ending in 5 or 0? In which case from 1 to 160 there are 80 numbers that end in 5 or 0 (5, 10, 15, 20, 25 etc). So fold 180.

Assuming everyone buys in multiples of 3, you’ll make £60.

80 bottles with 5 and zero means 400 tickets.

(If it were just zero you would need 800 tickets, but you gave 5 as well so half that. 3 for £1 means 800/3 = £266 takings approx.)

Oh ignore me…. You’ll need 400. Each multiple of 10 gets you 2 winning numbers ending in 5 or 0. Earning around £133

What the odds? Until you know that you won't know how many tickets you need.

Suppose you have a 1in 4 chance of winning you need 3 times as many tickets non winning tickets as you have winning ones

So 240 in total

And ignore me doing 800/3 when i had just said 400.

It is too cheap imo.

Do 50p each or 4 for £2. Yes I know that is the same but psychology gets people. (PTA experienced.)

Obviously you need to do this.
Use the right hand tickets to mark up the winners, then throw the other right hand tickets ending 1-4 and 6-9 away.
Then fold up all the left hand tickets.

You need 400 if you don’t include ticket 00, but 399 if you do. Whatever the case you need 400 tickets. This does not divide by 3 (as you are asking 3 for £1) so consider making it 81 bottles so you can make it up to 405 (or 404 if you start at 00).

Thank you all for your help. I don’t think I’ve explained it well. If you have 80 bottles and you use the 5s and 0s as the winning tickets, how do I work out, for example, 1 in 8 tickets winning a prize? And how many tickets do I need to put in the tombola?

In each block of 10 tickets 2 tickets will win a prize, so your odds of winning are 5:1.

You need 80 winning tickets, so you need at least 5x80 tickets in the tombola which is 400. However, you are selling the tickets in blocks of 3 so you actually need a number of tickets that will divide by 3 which means you need to fold 402 tickets.

You need to put ticket numbers 1 to 400 in. If numbers ending 5 and 0 win, then that’s a 1 in 5 chance. You can’t make it 1 in 8.

You can if you put extra tickets in that don't end in 5 or 0.....

For odds of 8:1 you would need to have a total of 640 tickets (but you would need to make sure that only 80 of them ended with 0 or 5)

Again, because you are selling in blocks of 3 you would probably need 639 or 642 to avoid being left with odd tickets.

If you wanted it to be 1 in 8 then it would have to be every eighth number that was a winner (so 8, 16, 24, 32, etc).

If it's numbers ending in 0s and 5s that are winners then that's every fifth number which would be a 1 in 5 chance of winning.

That’s it! This is how I thought it should be done. Thank you

You don't want to make it 1 in 8. Nightmare with the numbers.

Things you can do however to keep the profit high.
. Buy some cheap bottles (eg coke) to pad out the stall and stick at 1 in 5.
. Increase the price and keep at 1 in 5
. Turn it into 1 in 10

I would do 40p each or 5 for £2 (yes i know it is the same), and pad out with some cheaper bottles.

This would be horribly confusing for people though. With this sort of tombola it needs to be ending in 5 or zero, or just ending in zero, with resulting odds of 1 in 5, or 1 in 10.

And if you’re saying it’s 5 or 0 to win, people will assume they have a 1 in 5 chance. You can’t just put a load of extra non 5/0 tickets in to increase the odds.

Better to increase the price (50p per ticket or 5 for £2?), or do only zeros.

And if you’re saying it’s 5 or 0 to win, people will assume they have a 1 in 5 chance. You can’t just put a load of extra non 5/0 tickets in to increase the odds

Why not? I don’t think people rationally assess the chances of winning at at school fete. They're just donating what they can afford while taking the chance of winning a bottle of holiday liquer that's been in the cupboards of half the school over the last decade.

I think it's misleading as well.

Better to raise the price- £1 a ticket for a 1/5 chance of winning a bottle seems fine to me.

How much are the prizes worth? You need to cover the cost of the prizes plus whatever profit you want to make with the ticket sales.

They definitely do - I’ve heard lines of kids saying “it’s one in 5, I’m gonna win if I get another one” at the sweet jar stall tombola!
I mean, it’s low key and all basically fun ways of making donations and nobody really cares if they’re going to win the bad donated cheap wine or not, but I do think if you go with a sequentially numbered thing like raffle tickets, you have to use the implied odds there. If you want it to be one in 8, use coloured balls or something. Which wouldn’t work for a bottle tombola.

It's not misleading at all 🙄

If OP needs to meet the Gambling Commission rules then she just has to state the odds on a little sign somewhere.

So if it says "Tombola! 1 in 8 chance of a prize!" She's fine. If she doesn't need to meet GC rules then it's just "Tombola! Win a bottle with tickets ending in 5 or 0"

Some of you are really over-thinking this! 😂

Well it will be a good statistics teaching point that they're incorrect even if the odds are 1 in 5.

The odds of winning are one in five on average but for any individual having a relatively small number of turns, such as buying 5 tickets, they're nearly as likely to win nothing or two or even three prizes as they are one out of five.

It would be misleading to have 5 and 0 but then pad the draw out with other non winning tickets to make the odds 1 in 8 not 1 in 5.
It may be tempting but it isn't clear and transparent however tempting.

Personally I would just end in 0 and make the odds one in 10. It’s much easier that way. Then you need 800 tickets for 80 bottles. I would consider slightly upping the number of tickets, so maybe 4 for a £1. So you would make £200 if you sold all the tickets.

Obviously we know that! And they would experience that learning every time they re-queued to try and win sweets again! My point was that people, even kids, are well aware of the odds of tombolas, it’s hardly unusual.

I'm going for my dinner now and I'll come back to this later.