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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

The expected value is 1/probability is it not?

The matrix when computed should be 13.7

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

http://www.wolframalpha.com/input/?t=cr … 5%2F6))%5D

How is the expected value 1/probability?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

You did not enter the problem correctly

Matrix Inverse( IdentityMatrix[6] - {{0,1,0,0,0,0 }, {0,1/6,5/6,0,0,0} ,{ 0,0,1/3,2/3,0,0} ,{ 0,0,0,1/2,1/2,0} ,{ 0,0,0,0,2/3,1/3} , {0,0,0,0,0,5/6 }}).{{1},{1},{1},{1},{1},{1}} gives the right result.

If the probability is 1 / 6 of something happening then we expect it to happen once in 6 times.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

My result is correct. I just didn't sum the first row.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

When I entered yours it says the trace is 14.7. The trace is the sum of the diagonal elements. It may or may not be correct.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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The trace and the sum of the first row are the same for that matrix.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Yes, but are you sure that will always be the case?

This way spits the answer out in a form that is easy to understand.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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No, I sum the first row. WA is the one who thinks you need the trace.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

When I run your link, I get this result. That is clearly not the right answer.

For one thing he did not interpret the identitymatrisx command correctly. For another the inverse was not calculated...

I would do it the way I showed in post#128.

Taking a little break.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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That is not the same result I am getting when I press the link.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Supposing others get my result? Isn't my way more reliable, since we are both getting the same answer. Also, my syntax is much closer to the package's syntax.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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You just had multiplication by the vector (1,1,1,1,1,1) and I did the multiplication by hand. It is the same method.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

I am talking about the syntax of the commands.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

New problems?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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** A deck of cards are dealt out in a circle. What is the expected number of pairs of adjacent cards which are both black?**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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A standard French deck?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

It is a regular deck of playing cards.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Okay.

What do you get as the answer for decks of 4 and 6 cards (half of which are black)?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

E(4 card deck) = 2 / 3

E(6 card deck) = 6 / 5

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

And E(8)?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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E(8 card deck) = 12 / 7

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I haven't been able to find a solution...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

Okay, I can give the answer if you want it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,507

I'd rather get a method than an answer, but either is okay...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,210

Hi;

I'd rather get a method than an answer,

Hmmmm. You should already have the answer or darn close to one. Have you forgotten how we work?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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