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#1 2013-03-24 00:28:49

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Shared birthdays

What are the chances that 6 people celebrate their Birthday in the same 2 months? Assume all months are equal.

Last edited by anna_gg (2013-03-24 01:27:25)

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#2 2013-03-24 01:09:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi;

Last edited by bobbym (2013-03-24 01:13:40)


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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#3 2013-03-24 01:28:11

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Shared birthdays

bobbym wrote:

Hi;

See my corrected description.

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#4 2013-03-24 01:48:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi;

That is a little different. I hope I am understanding what you want. It seems you want all six people to have their birthdays in only two months.

For that I am getting.


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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#5 2013-03-28 01:42:08

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Shared birthdays

Right smile

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#6 2013-03-28 11:24:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi;

Whamo! Wunderbar! Doron Zeilberger eat your heart out. Am I the king of comby/proby or what?


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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#7 2013-03-28 11:50:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

How'd you get that answer?

And, I am pretty sure his last name is Zielberger.


“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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#8 2013-03-28 11:51:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi;

No, it is Zeilberger. The way I get all the answers I get.


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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#9 2013-03-28 11:56:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

Yes. I permuted the i and the e. It seems to be common with me. I have a tough time remembering whether it's Liebniz or Leibniz.

Direct count?


“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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#10 2013-03-28 12:05:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

No, all combinatoric problems fall into categories. Surely you have read the 12 fold way or even better the 30 fold way. I have my own set in addition to those. These templates help solve many types of problems.


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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#11 2013-03-28 12:12:58

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

Would you mind sharing?


“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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#12 2013-03-28 12:20:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Of course you were half right I already had the answer before I even began.

Of course, I will put down the formula-template here.


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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#13 2013-03-28 12:23:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

Great, thank you!


“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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#14 2013-03-28 12:33:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

This looks like some of Feller's work or maybe Rose, I am not sure.

Surely you recognize that?!


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.

Offline

#15 2013-03-28 22:54:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

What the hell is that?


“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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#16 2013-03-28 23:18:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Looks like a formula! So you do not recognize 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.

Offline

#17 2013-03-28 23:32:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

It looks like some stuff I've seen on Wiki's distributions pages.


“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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#18 2013-03-28 23:33:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Better than that. With that you compute the answer to anna's problem quickly.


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.

Offline

#19 2013-03-30 04:58:00

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Shared birthdays

I will try to share my solution in a more explanatory way (Sorry, Bobby, I don't imply that yours is not easy to understand - it is just that I am a novice and not very familiar with complicated solutions!!):
We first must calculate all the possible ways to get 2 months out of 12, that is

Then we must calculate all the different ways by which we can arrange the birthdays of 6 people in these 2 months: Either 5 people have their birthday in the first month and 1 in the second, or 4 in the first and 2 in the second etc. Obviously we do not consider the case of 0/6 or 6/0. For the first case, we first get 1 out of 6 (for the first person’s birthday) and then for the second person’s it will be 5 out of 5, and so on.
Here is the calculation:

The total probability is the product of the first two (66 x 62) divided by the total number of all different ways by which 6 people can have their birthdays in 12 different months, that is, 12^6.

So we have

Last edited by anna_gg (2013-03-30 04:58:57)

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#20 2013-03-30 05:11:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi anna_gg;

Sorry, Bobby, I don't imply that yours is not easy to understand

No problem. I am glad to see your solution. Also, anyone who can do that problem I do not characterize as a novice.

Have you tried Codecogs?


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.

Offline

#21 2013-03-30 05:57:52

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Shared birthdays

No I haven't; actually I wrote the solution in a Word doc, but when I copied it here, the formatting was screwed up sad(

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#22 2013-03-30 06:35:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi anna_gg;

I latexed it up for you.

When you have time try this site

http://latex.codecogs.com/editor.php

perfect math every time!


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.

Offline

#23 2013-03-30 07:35:15

anna_gg
Member
Registered: 2012-01-10
Posts: 113

Re: Shared birthdays

Thank you! Very useful!

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#24 2013-03-30 08:04:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,965

Re: Shared birthdays

Hi;

You are welcome and happy latexing.


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.

Offline

#25 2013-03-30 10:35:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Shared birthdays

Hm, then the solution for n people seems to be 66*(2^n-2)/(12^6).

And thank you both for showing your methods.


“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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