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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,590

The expected value is 1/probability is it not?

The matrix when computed should be 13.7

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

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: 88,590

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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: 88,590

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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: 88,590

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.

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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: 88,590

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.

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**anonimnystefy****Real Member**- From: The Foundation
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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
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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.

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**anonimnystefy****Real Member**- From: The Foundation
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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
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Hi;

I am talking about the syntax of the commands.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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
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Hi;

It is a regular deck of playing cards.

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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
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E(4 card deck) = 2 / 3

E(6 card deck) = 6 / 5

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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And E(8)?

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

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**anonimnystefy****Real Member**- From: The Foundation
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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
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Hi;

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

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**anonimnystefy****Real Member**- From: The Foundation
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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: 88,590

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?

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