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#76 2013-04-01 00:02:31

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,884
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Re: rat run probability

What is that formula about?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#77 2013-04-01 00:09:52

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

He used Bayes theorem to find the answer without simulation. It is 1 / 13 , verified by simulation.


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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#78 2013-04-01 00:11:40

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,884
Website

Re: rat run probability

How do you use Bayes Theorem?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#79 2013-04-01 00:17:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

It is pretty much a plug in to a formula. We will need the solution to a which is 2 / 13 and some notation. Ready?


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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#80 2013-04-01 00:20:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

You also need the solution to b).


“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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#81 2013-04-01 00:22:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

b) he has by a nice piece of reasoning to be 1 / 2.


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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#82 2013-04-01 00:26:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

I saw it. But I am not sure it must be true. How do you know that all exits have the same probability of being exited through?


“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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#83 2013-04-01 00:29:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

I checked his answer using a markov chain and it also agreed with his simulation.


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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#84 2013-04-01 00:34:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

I am not saying that the answer of 1/2 is not correct. Just that the reasoning you guys used might not be sound (I am referring to the one where you claim that the probability is 1/2 because two halves of the exits are on 3).


“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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#85 2013-04-01 00:40:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

The simulation and the Markov chain is what I base the 1/2. But his idea does appear to work.


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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#86 2013-04-01 00:55:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

d)i) seems to be around 0.246...


“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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#87 2013-04-01 01:01:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

You might be right I do not know yet.


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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#88 2013-04-01 01:03:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

The number's are varying a lot. I am getting stuff from 0.246 to 0.2464 .


“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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#89 2013-04-01 01:07:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

If that is a simulation, that is not a big variation.


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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#90 2013-04-01 01:09:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

I bigger one (10 million tries) gave 0.246225.


“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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#91 2013-04-01 01:11:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

You can easily determine the accuracy of that answer.


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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#92 2013-04-01 01:13:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

How?


“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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#93 2013-04-01 01:19:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

You can be pretty sure that the true answer lies between those two numbers,


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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#94 2013-04-01 01:24:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

Why 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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#95 2013-04-01 01:26:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

It is based on statistics using the standard deviation.


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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#96 2013-04-01 01:32:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

Anyway... Do you have an idea what the exact answer might be?


“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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#97 2013-04-01 01:38:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

Hi;

Not yet, I am swamped right now and have not looked at 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

#98 2013-04-01 02:30:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: rat run probability

Okay. Post if you get anything...


“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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#99 2013-04-01 06:43:20

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,884
Website

Re: rat run probability

bobbym wrote:

Ready?

Yes!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#100 2013-04-01 08:15:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,638

Re: rat run probability

Hi Agnishom;

I am sorry but I have completely forgot what we were going to go over.


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

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