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#1 2013-04-16 01:05:36

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,193
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Marbles without replacement (probability)

A bag contains 10 red marbles, 10 green marbles, 10 yellow marbles and 10 blue marbles. You reach into the bag and grab a marble, then reach into the bag and grab a second marble. The probability that the second marble is the same color as the first marble is a/b, where a and b are positive, coprime integers. What is the value of a+b?

Note: You do not place the first marble back into the bag.

Is it 9/39?? But they tell it is wrong


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2013-04-16 01:24:43

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi;

Yes, that answer is wrong.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-04-16 01:28:25

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,193
Website

Re: Marbles without replacement (probability)

Why? sad


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2013-04-16 01:37:20

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Supposing that answer were correct in some way, does it answer this question.

a/b, where a and b are positive, coprime integers


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-04-16 01:44:59

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,193
Website

Re: Marbles without replacement (probability)

sad O sad!
Thanks btw


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2013-04-16 01:51:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Everything checking out now?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2013-04-16 02:07:58

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,193
Website

Re: Marbles without replacement (probability)

Yes


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#8 2013-04-16 02:13:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Probability and combinatorics are the toughest things in mathematics. The best of the best can often make mistakes. We are going to make more mistakes.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2013-04-26 22:11:43

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

An addition to the question in #1:

What's the expected number of marbles to be picked till we get two marbles of the same color?


"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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#10 2013-04-26 22:46:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2013-04-26 23:22:30

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi bobbym,


"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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#12 2013-04-26 23:30:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#13 2013-04-26 23:53:41

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi,

But answer must be independent of the number of marbles, isn't it?


"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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#14 2013-04-27 00:07:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi;

The draw is without replacement so the probability changes on each draw.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#15 2013-04-27 00:35:59

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

That makes sense.
I think the way I thought is wrong, I first picked up 5 marbles and then calculated my answer from there.
I forgot to consider the probability of obtaining those subsets.


"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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#16 2013-04-27 00:39:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi gAr;

I adjusted the latex answer in post #12.

I have to get some sleep, see you later.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#17 2013-04-27 00:42:16

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi bobbym,

Okay, take rest, see you later..
Read my above reply when you are back.


"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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#18 2013-04-27 00:43:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Thanks and thanks for coming in with a good problem.

Did you mean post#15?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#19 2013-04-27 17:22:32

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi bobbym,

I tried the problem again


"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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#20 2013-04-27 17:28:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi gAr;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#21 2013-04-27 18:16:56

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi bobbym,

I think it's correct.

The addition looks good to me:


"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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#22 2013-04-27 18:38:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi gAr;

This is what I did;


The boxed part is incorrect. There is no winner for one throw!

Correct answer 30008/9139.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#23 2013-04-27 19:00:39

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Hi,

Do we need to include 1?
Because we need at least two marbles to check whether they are of the same color?


"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."

Offline

#24 2013-04-27 19:02:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,199

Re: Marbles without replacement (probability)

Hi gAr;

We were both posting at the same time. Check post #22.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#25 2013-04-27 19:05:47

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Marbles without replacement (probability)

Yes, now it's all right!


"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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