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#1 2014-04-03 23:03:10

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Probability-1


A pack of forty cards numbered 1-10 and four suits are well shuffled and placed face up on the floor.
After placing the cards sequentially, the positions are numbered like this
[1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5]
A card numbered 1 must not occupy a position numbered 1, and same restriction for cards 2-7. Cards 8-10 are free to be placed anywhere.
What's the probability of such an arrangement?

Last edited by gAr (2014-04-05 01:02:10)


"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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#2 2014-04-04 05:06:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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 2014-04-04 05:50:48

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi,


"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

#4 2014-04-04 15:07:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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.

Offline

#5 2014-04-04 17:07:00

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi,


"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

#6 2014-04-05 00:48:04

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

Re: Probability-1

Hi gAr

Shouldn't the positions be numbered 1,2,3,4,5,6,7,0,1,2,…?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#7 2014-04-05 00:59:18

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Mmm, yes. I wanted to tell 1+ (pos# mod 7), I overlooked 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."

Offline

#8 2014-04-05 01:01:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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.

Offline

#9 2014-04-05 01:03:23

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

Re: Probability-1

gAr wrote:

Mmm, yes. I wanted to tell 1+ (pos# mod 7), I overlooked it.

Ah, okay then. I wasn't sure which definition to hold true. Thanks for the clarification.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#10 2014-04-05 01:10:36

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

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."

Offline

#11 2014-04-05 01:15:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi gAr;


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.

Offline

#12 2014-04-05 01:16:29

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Ah, okay then. I wasn't sure which definition to hold true. Thanks for the clarification.

You're welcome.


"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

#13 2014-04-05 01:18:28

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

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."

Offline

#14 2014-04-05 06:11:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi gAr;


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.

Offline

#15 2014-04-05 06:24:30

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Re: Probability-1

Why don't you use a simulation first? I am getting

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#16 2014-04-05 06:29:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi ShivamS;


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.

Offline

#17 2014-04-05 06:49:42

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Re: Probability-1

Close, but still wrong... I think my algorithm is correct, but I probably made a mistake in my code.

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#18 2014-04-05 07:43:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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.

Offline

#19 2014-04-05 07:45:18

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Re: Probability-1

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#20 2014-04-05 08:04:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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.

Offline

#21 2014-04-05 08:06:11

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

Re: Probability-1

Great! Now time to find some algebraic method.

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#22 2014-04-05 15:17:32

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

Hi ShivamS,

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."

Offline

#23 2014-04-05 15:51:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi gAr;


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.

Offline

#24 2014-04-05 16:02:00

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Probability-1

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."

Offline

#25 2014-04-05 16:44:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,715

Re: Probability-1

Hi;


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.

Offline

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