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#1 2013-01-23 14:48:49

cooljackiec
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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
lol

#2 2013-01-23 15:45:31

bobbym
Administrator

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Re: Probability!

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-09-06 09:45:44

Anynomous
Guest

Re: Probability!

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

#4 2013-09-06 10:19:35

anonimnystefy
Real Member

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Re: Probability!

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

Code:

(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 (2013-09-06 10:20:32)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-09-06 10:38:43

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-09-06 10:47:39

anonimnystefy
Real Member

Offline

Re: Probability!

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-09-06 10:58:36

anonimnystefy
Real Member

Offline

Re: Probability!

Here's a simulation that confirms 13/14:

Code:

(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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#8 2013-09-06 11:10:56

bobbym
Administrator

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2013-09-06 11:14:20

anonimnystefy
Real Member

Offline

Re: Probability!

Okay. See you later.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10 2013-09-06 14:21:59

Fruityloop
Full Member

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Re: Probability!

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


The eclipses from Algol (an eclipsing binary star) 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.

#11 2013-09-06 17:01:59

bobbym
Administrator

Offline

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#12 2013-09-07 20:10:28

ElainaVW
Full Member

Offline

Re: Probability!

Hello;

Code:

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

#13 2013-09-07 21:56:05

bobbym
Administrator

Offline

Re: Probability!

For the other M:

Code:

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

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-09-08 01:22:04

gAr
Star Member

Offline

Re: Probability!

Maxima:

Code:

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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