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#1 2011-03-30 15:23:17
- chineseballer06
- Member
- Registered: 2011-02-01
- Posts: 34
Roulette Probability
Hi everyone, I am having difficulty with this problem any help is greatly appreciated.
In European roulette the ball lads on one of the numbers 0,1,...,36 in every spin of the wheel. A gambler offers at even odds the bet that the house number 0 will come up once in every 25 spins of the wheel. What is the gambler's expected profit per dollar bet?
If you can help me figure out which distribution to use that would help a lot, thanks again!
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#2 2011-03-30 18:56:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Hi chineseballer06;
The chance that the ball lands on a 0 at least once in 25 spins is .49589. He loses approximately .82 cents ( not quite a penny ) on every dollar bet.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2011-03-31 05:12:28
- chineseballer06
- Member
- Registered: 2011-02-01
- Posts: 34
Re: Roulette Probability
Hi bobbym
What distribution did you use to get that? I don't know if this helps but in class we are learning about discrete distributions like Poisson, Bernouilli, and geometric distributions.
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#4 2011-03-31 05:32:10
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Hi chineseballer06,
I did it like this:
P(at least one 0) = 1 - P(no 0) = 1−(36/37)^25 ≈ 0.4958968
Hence expected gain ≈ 0.4958968*($1) + (1-0.4958968)*(-$1) = −$0.0082064
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#5 2011-03-31 06:30:01
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Hi chineseballer06;
gAr did it like I did. But if you must know the distribution that fits that type of problem is the binomial distribution. You should have covered that first. By the way that bet is a loser so make sure you are betting the don't.
Hi gAr, I did not get a chance to talk you today.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2011-03-31 08:30:30
- chineseballer06
- Member
- Registered: 2011-02-01
- Posts: 34
Re: Roulette Probability
Okay thanks everyone!! That really helped! 
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#7 2011-03-31 10:09:15
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Hi;
You are welcome.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#8 2011-03-31 19:42:19
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Hi chineseballer06,
You're welcome.
Hi bobbym,
No problem. I didn't have anything interesting to talk about.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#9 2011-03-31 19:54:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Hi gAr;
That has never stopped me. I did not do much math yesterday, too tired from the shopping.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2011-03-31 20:06:30
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Hi bobbym,
... too tired from the shopping.
Are you picky? Or was it the crowd?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#11 2011-03-31 20:10:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Crowd mostly. I did not have much choice so I was not picky. Then I had to carry the whole thing home. Only weighed 19 lbs but it got heavier each block.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2011-03-31 20:19:11
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Ok.
I too dislike crowd.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#13 2011-03-31 20:22:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
We do not have as large a population as your country but our cities are very crowded. We pack a lot of people into a very small area.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2011-03-31 20:52:07
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
The place I live at the moment is away from the city, hence less crowd and traffic.
Major cities here are awfully crowded. But white-collared jobs are mostly available only there, so I'll also be doomed to end in such place!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#15 2011-03-31 20:57:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Doomed is a good word. I like the country but I have spent my entire life in big cities. Crowds, pollution, noise, crime, rats, filth and cars everywhere. Not a blade of grass or a tree that does not get pulled out so they can pave another road or build another mall.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2011-03-31 21:05:55
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
And soon they will start selling oxygen!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#17 2011-03-31 21:07:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
They already do in Britain and elsewhere. It is sort of a novelty at the moment but...
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2011-03-31 21:24:10
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Yes, we can only look around at people doing stupid things. Who will listen to us 
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#19 2011-03-31 21:28:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
No one. You can only improve yourself. You can only steer your own course. Here I try to lose myself in math and computers and ignore what goes on outside.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2011-03-31 21:35:11
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
I do the same thing!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#21 2011-03-31 21:38:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Forums are a way to maybe do a little bit of help. If you can stand the moderators.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#22 2011-03-31 21:47:29
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Forums are a great way to help. And what's up with the moderators?!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#23 2011-03-31 21:50:53
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
Just a joke. I actually thought that was funny.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#24 2011-03-31 21:57:55
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Roulette Probability
Ok, got the joke, wanted to confirm.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#25 2011-03-31 22:04:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Roulette Probability
I am going to take a little break, see you later.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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