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In a cookie jar, there are 6 chocolate chip cookies and 8 oatmeal cookies. Hungry Paddy takes out the cookies one at a time and proceeds to eat them. The probability that the 7th cookie that Paddy eats is a chocolate chip cookie is a/b, where a and b are positive coprime integers. What is the value of a+b?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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Thanks but how to do?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Hi;

This sort of tells you it doesn't matter what number you pick to eat a chocolate chip cookie.

Actually this is a trick question and no computation at all is required to solve it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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How did you get into that formula?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

It is really just a joke but I used the box model. It is unnecessary!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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Why should it be a joke?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Because it is a trick question and using a computational idea on it just shows how stupid I am.

I ask you this what is the probability that the 15 th card from the top of a standard deck is a 5?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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So how do you answer that question? I am still clueless

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

What is the chance that the top card of the deck is a 5?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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1/52

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

That would be a particular 5 like the 5 of spades. There are 4 fives. Please recompute the answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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1/13 ?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

That is correct. Now you see that the 15th card is just the same as the top card.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

If someone phrases the question a little bit different, I bring in the heavy machinery. No wonder my back is bad.

Confucius says,"Don't use a cannon to kill a mosquito."

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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The fiftteenth card isn't the same as the first. If any of the previous fourteen were a five, then the fifteenth could not have been a five

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

You have no information like that. The 15th card has the same amount of information that the first card has. For instance, if I count down to the 15 th card and put it on top has it's probability changed?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I am intrigued by this problem.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Just understand that it is the card problem reworded. It can be verified by the above calculation or by enumeration. The probability is always the same.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Yes, I know. I read the discussion.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

I just have to convince Agnishom and he can be a toughie.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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bobbym wrote:

The fifteenth card has the same amound of information

Nope. When you have gone down to the fifteenth card you already have the information of the fourteen cards above

*Last edited by Agnishom (2013-04-14 02:29:00)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

What information do you have about it? You do not look at the first 14 cards.

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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There are many different ways in which it can turn out to be a five.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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