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## #1 2013-01-22 15:48:49

cooljackiec
Member
Registered: 2012-12-13
Posts: 185

### Probability!

I have a bag with 5 pennies and 3 nickels. I draw coins out one at a time at random. What is the probability that I haven't removed all 3 nickels after 4 draws?

I tried 1/2 and 11/14. They are wrong

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

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## #2 2013-01-22 16:45:31

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,801

### Re: Probability!

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 2013-09-05 11:45:44

Anynomous
Guest

### Re: Probability!

This solution is not right, i tried it. Can you show how you got it, or something

## #4 2013-09-05 12:19:35

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

### Re: Probability!

I think he might be right. I am getting 13/14.

``(Select[Permutations[{p, p, p, p, p, n, n, n}], Count[Take[#, 4], n] < 3 &] // Length)/(Permutations[{p, p, p, p, p, n, n, n}] // Length)``

Last edited by anonimnystefy (2013-09-05 12:20:32)

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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## #5 2013-09-05 12:38:43

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,801

### Re: Probability!

Hi all;

That is all the ways to draw 4 coins from 5 and 3. There are 15 total ways and four winners. So I will have to go with 11 / 15 jist as before. Also, the OP already verified this.

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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## #6 2013-09-05 12:47:39

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

### Re: Probability!

But, the probabilities of those 4-draws are not all the same.

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 2013-09-05 12:58:36

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

### Re: Probability!

Here's a simulation that confirms 13/14:

``````(Table[If[Count[
Delete[Delete[
Delete[Delete[{p, p, p, p, p, n, n, n}, RandomInteger[{1, 8}]],
RandomInteger[{1, 7}]], RandomInteger[{1, 6}]],
RandomInteger[{1, 5}]], n] > 0, 1, 0], {100000}]//Total)/100000//N``````

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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## #8 2013-09-05 13:10:56

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,801

### Re: Probability!

Hooohaa as the great Al Pacino would say. You have provided some good evidence, I will rethink the whole thing as soon as I come back.

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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## #9 2013-09-05 13:14:20

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

### Re: Probability!

Okay. See you later.

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 2013-09-05 16:21:59

Fruityloop
Member
Registered: 2009-05-18
Posts: 135

### Re: Probability!

I think the answer is 13/14.
(5C4*3C0 + 5C3*3C1 + 5C2*3C2)/8C4 = 13/14.

The eclipses from Algol come further apart in time when the Earth is moving away from Algol and closer together in time when the Earth is moving towards Algol, thereby proving that the speed of light is variable and that Einstein's Special Theory of Relativity is wrong.

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## #11 2013-09-05 19:01:59

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,801

### Re: Probability!

Hi;

Yes, that is the correct answer. Verified by the using the hypergeometric distribution.

Thank you spotting that everyone.

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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## #12 2013-09-06 22:10:28

ElainaVW
Member
Registered: 2013-04-29
Posts: 577

### Re: Probability!

Hello;

``````Probability[x < 3,
x \[Distributed] HypergeometricDistribution[4, 3, 8]]``````

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## #13 2013-09-06 23:56:05

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,801

### Re: Probability!

For the other M:

``Probability(RandomVariable(Hypergeometric(8, 3, 4)) < 3)``

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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## #14 2013-09-07 03:22:04

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

### Re: Probability!

Maxima:

``sum(pdf_hypergeometric(i,3,5,4),i,0,2);``

"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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