Need help with figuring out the chances of a raffle :)

[Callahan121]

Hello guys,

so I've been having problems with figuring out what are my chances of winning a raffle.

There are 5555 raffle tickets and 50 winners.
I hold 55 raffle tickets.
What are my chances in terms of percentages?

This seems easy, but I just can't wrap my head around it haha.
Thank you so much in advance!

 

[Deleted member 4993]

Hello guys,

so I've been having problems with figuring out what are my chances of winning a raffle.

There are 5555 raffle tickets and 50 winners.
I hold 55 raffle tickets.
What are my chances in terms of percentages?

This seems easy, but I just can't wrap my head around it haha.
Thank you so much in advance!

In how many ways can you draw 5 tickets, out of 5555, - without any restriction?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[blamocur]

Hello guys,

so I've been having problems with figuring out what are my chances of winning a raffle.

There are 5555 raffle tickets and 50 winners.
I hold 55 raffle tickets.
What are my chances in terms of percentages?

This seems easy, but I just can't wrap my head around it haha.
Thank you so much in advance!

Which chances? Of at least one winning ticket? Of exactly one winning ticket?

 

[Dr.Peterson]

Hello guys,

so I've been having problems with figuring out what are my chances of winning a raffle.

There are 5555 raffle tickets and 50 winners.
I hold 55 raffle tickets.
What are my chances in terms of percentages?

This seems easy, but I just can't wrap my head around it haha.
Thank you so much in advance!

Assuming you want the probability of winning at least one prize, the easiest way to find it is to first find the probability that you don't win any prize. What is the probability that all your tickets are losers?

Show us your attempt, or any ideas you have, so we can see what you have learned and where you need help. In particular, I'd like to see what you know about combinations.

 

[Callahan121]

Well, I want to know what are the chances of winning AT LEAST one prize if there are 50 prizes and I own 55 raffle tickets out of 5555.

To be completely honest, I'm in Crypto and NFT investing so I would really love to learn more about combinations and doing math when it comes to figuring out a chances of something happening.

Like ok, if I own 1 raffle ticket, I would have 50/5555 chances of winning, right?
Which would be 0,90%.

But if I own 50, do I first have to do 50/5555 (which is 0,0090) and then multiply that with 50 (my tickets?).
Which would be 0,45 (45% chances of winning at least one prize)?

Is that right?

Thank you guys so much!

 

[Steven G]

But if I own 50, do I first have to do 50/5555 (which is 0,0090) and then multiply that with 50 (my tickets?).
Which would be 0,45 (45% chances of winning at least one prize)?

Is that right?

Let's go with that idea. What if you bought 1000 tickets, then 1000*(50/5500)>1. No probability can be greater than 1 = 100%!!
So no, that method does not work.

 

[Callahan121]

Assuming you want the probability of winning at least one prize, the easiest way to find it is to first find the probability that you don't win any prize. What is the probability that all your tickets are losers?

Show us your attempt, or any ideas you have, so we can see what you have learned and where you need help. In particular, I'd like to see what you know about combinations.

I have replied above.

 

[Callahan121]

Let's go with that idea. What if you bought 1000 tickets, then 1000*(50/5500)>1. No probability can be greater than 1 = 100%!!
So no, that method does not work.

Hmm. Ye, that's true. So what would be the correct method? If you can help.

 

[Steven G]

Here is basically what Dr Peterson is saying.

100% of the time you will have no winning tickets or exactly one winning ticket or exactly two winning tickets or exactly three winning tickets or exactly four winning tickets or exactly five winning tickets.
Note that 100% = 1

So P(0 winning tickets) + P(1 winning ticket)+ P(2 winning tickets) + P(3 winning tickets)+ P(4 winning tickets) + P(5 winning tickets) = 1

You want what is in bold. That is, P(1 winning ticket)+ P(2 winning tickets) + P(3 winning tickets)+ P(4 winning tickets) + P(5 winning tickets) = 1 - P(0 winning tickets).

It is easier to find one probability (P(0 winning tickets)), then it is to find five probabilities ( P(1 winning ticket), P(2 winning tickets), P(3 winning tickets), P(4 winning tickets), P(5 winning tickets)), so computing 1 - P(0 winning tickets) is the way to go.

 

[Dr.Peterson]

Like ok, if I own 1 raffle ticket, I would have 50/5555 chances of winning, right?
Which would be 0,90%.

But if I own 50, do I first have to do 50/5555 (which is 0,0090) and then multiply that with 50 (my tickets?).
Which would be 0,45 (45% chances of winning at least one prize)?

Is that right?

Thank you guys so much!

The number of tickets is large enough, compared to your tickets, that this isn't too far off; but it does overestimate.

Would you like to tell us how much you know about probability (and perhaps why you asked this particular question, if you are not studying the subject)? That would give us a starting point in helping you. But we don't generally try to teach a subject from scratch; if you know nothing about combinations and how they relate to a question like this, then you really need to read up on it and then come back with an attempt, so we can work with you.