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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

here's a problem given to me by a professor of mine:

If two players are playing a game in which they draw one card each from two separate decks (shuffled) then what's the probability that they will draw at least one same card?

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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: 89,150

Same type, ace, ten? Or exactly ace of hearts etc.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

hi bobbym

exactly the same card.they have two standard decks without the jokers.

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: 89,150

Okay, thanks for that informatiuon. I am working on it.

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

how's it coming on bobbym?

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: 89,150

It is a standard problem, your professor is not very imaginative. Unfortunately I threw my solution away so please hold.

**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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**TMorgan****Member**- Registered: 2011-04-13
- Posts: 25

Do you mean on the first draw or do they work their way all through the decks?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

hi bobbym

he didn't make it up.i think this problem was on a high school competition.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,611

hi TMorgan

i mean through the decks.so if at any moment they draw the same card then it is a wanted event.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

**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: 15,611

how did you get that?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Is it right?

**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: 15,611

i think it is,but i am not sure.how did you get it?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

It is a standard derangement problem. Solved long ago. The probability of no fixed points in a permutation of {1,2,3,4,...n} approaches 1/ e.

**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: 15,611

well how do you get the first probability,the 1-1/e one?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

That is not important because that is only an approximate answer. That is why I asked if you knew.

The exact answer I believe is:

The dn operator stands for the number of derangements.

The question was posed by Montmort in 1781 and answered by him and Bernoulli.

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

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