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#1 2013-01-31 12:40:55

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Please Post By 10:30 Eastern Time!!!

A bag has marbles of 4 colors: red, white, blue, and green. Assume that if we take four marbles out at random (without replacement), each of the following is equally likely:

(1) one marble of each color is chosen,

(2) one white, one blue, and two reds are chosen,

(3) one blue and three reds are chosen,

(4) all four are red.

What is the smallest possible number of marbles in the bag?


I see you have graph paper.
You must be plotting something
lol

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#2 2013-01-31 20:56:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

Re: Please Post By 10:30 Eastern Time!!!

Hi;

Sorry, I could not meet the time, I was sleeping.

The smallest I can come up with is a bag containing 11 reds, 3 whites, 2 blues and 5 greens.


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 2013-02-01 11:48:49

cooljackiec
Member
Registered: 2012-12-13
Posts: 160

Re: Please Post By 10:30 Eastern Time!!!

Its okay, I got 21


I see you have graph paper.
You must be plotting something
lol

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#4 2013-02-01 18:45:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

Re: Please Post By 10:30 Eastern Time!!!

Sorry, that is what I got too, I meant 3 whites not 4!


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 2014-02-06 14:11:48

Tpetrie01
Guest

Re: Please Post By 10:30 Eastern Time!!!

Sorry, I know this post is old - but can you give me a hint as to how you figured this problem out, bobbym? I've got a similar problem and i want to know which direction i should be thinking in.

#6 2014-02-06 14:20:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

Re: Please Post By 10:30 Eastern Time!!!

Hi;

You would use the multivariate hypergeometric distribution. After that you would try it until you found the right number. This would require some trial and error best done by computer.


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 2014-02-06 14:39:40

Tpetrie01
Guest

Re: Please Post By 10:30 Eastern Time!!!

Thanks! This helps a lot.

#8 2014-02-06 14:42:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,247

Re: Please Post By 10:30 Eastern Time!!!

You know how to use the multivariate hypergeometric?


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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