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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

Hi!!!I hope you can help me at the following exercise:

We have a container that contains r balls that have numbers 1,...,r. We choose at random n of them without replacement. Let Y be the greatest and Z the smallest of the numbers of the balls we chose. Which are the probabilities P(Y<=y) and P(Z>=z)????

Thanks in advance!!!!!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Hi;

Where does the problem come from? What textbook?

**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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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

The problem comes from the book:Introduction to Probability Theory(P.HOEL,S.PORT,C.STONE)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Hi;

Page and number please?

**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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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

It is in the capital 3,the exercise 12....

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Hi;

Okay, thank you. I will work on it? Do you have anything that can help?

**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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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

I think I have to use {n choose r},but I am not sure

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

I am getting

*Last edited by anonimnystefy (2013-04-14 01:52:06)*

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

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**evinda****Member**- Registered: 2013-04-13
- Posts: 105

And how can I prove this???

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Well, I used the inclusion-exclusion principle on the negative event.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Ooooh that is nice one. I have a better question... Where did you get it from?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Get what from?

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Ooooh that is a good one! You are in good form today. What? I certainly did not mean the Eiffel tower. The equation, I do not know it. So I figure it is some book that I skipped over.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

It can be found in any common textbook. |AuB|=|A|+|B|-|AnB|.

*Last edited by anonimnystefy (2013-04-14 01:36:35)*

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Which common one would you recommend?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Well, I do not know of any you could read, but there is an article on Wikipedia on it. Search for "inclusion exclusion principle".

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

The Wikipedia article covers PIE but it does not explain the formula in post #8.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

No, I derived the formula myself using the PIE.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Hmmm, have you tested this formula?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Hm, I just found an error concerning the numbers. Let me fix the formula.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

Did you fix it? Now how about a verification?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

Which kind of verification do you need?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

We could run a simulation. We could substitute numbers and at least see whether the formula works for a few examples. It can not prove the correctness of it but it sure can prove it false.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,603

I tested for a few values and it works.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,714

M code please?

**In mathematics, you don't understand things. You just get used to them.**

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