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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

You were going to do Bayes' theorem.

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: 86,666

I remember that now but Agnishom has probably gone to sleep.

Here is the formula for Bayes theorem

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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What does the notation

mean?'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

P(A|B) is the probability that A has happened if we know that B has happened.

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

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Got it from the wiki,

Thank You

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,666

Hi Agnishom;

This problem uses what we already have solved from b) and a) to solve question c).

I used a markov chain just like the one I showed you but bigger to get a and b.

Then it is just a plugging in to a formula.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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bobbym wrote:

Then it is just a plugging in to a formula.

Are you talking about c?

And why do you need Markov Chains for b), it comes by simple logic

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,666

Hi;

Yes I am talking about c.

it comes by simple logic

It is very important in mathematics to get an answer by using more than one method. I often see people putting answers down from a single method sure that they are right. It is much more certain that you have the correct answer when it has come from several different ideas or methods. We got 1 / 2 by a Markov chain, a simulation and reasoning. I am now very sure of that answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Oh yeah!

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

Hi Agnishom

I am not sure about your reasoning for b. Not all the exits might have the same probability of being exited through.

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: 86,666

Hi;

For d) i) I am getting:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Hi stefy;

Why shouldn't it be so? You can treat the whole system of rooms as a whole since the mouse can randomly move within it. Now since the probability of being in any of the three rooms is the same, it can exit through any exit with the same probability

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

Hi bobbym

So, I was close.

Hi Agnishom

The real question is why it should be. How do you know all the doors are equally likely to be exited through, besides intuition?

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: 86,666

Hi;

Because after the initial move from the space outside the maze, each room is equally likely because there is the same number of entrances from the other room.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Moreover, according to the problem, in a room with multiple exits, every exit has the same probability of being exited through

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,666

Yes, since the prob of being in any room is the same it is only natural that exits from 3 would equal exit from 1 and 2.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

The simulation does approve of the equality, but I am not very convinced by the reasoning.

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: 86,666

Yes, but there must be something to it or else it is an amazing coincidence. Physicists believe in random events and coincidence, I do not.

We will go with the simulation and the Markov chain if that makes you feel more secure.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,523

It does. I am not saying the reasoning is wrong, though. It is probably legit.

And, I ran a simulation with 2 doors between 1 and 2. Didn't change much.

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: 86,666

That is odd, it is why I stay away from combinatoric reasoning. Some say, because I stink at it. They are partially right. I think it can be misleading sometimes and confusing the rest of the time. I prefer computation. Numbers do not lie unless they are describing the US economy.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

I'm getting 7 / 16 for (ii)

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,666

We stopped at i) I think I was getting tired.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, verify when you are done.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,666

Hi gAr;

I am going to eat, I am starving. Will see you in a bit.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

And got 56 / 63 for (iii)

Conditional probability is posing a problem to simulate, hmmm!

Okay, eat well. I may go to sleep in a while, see you "tomorrow".

*Last edited by gAr (2013-04-04 06:14:46)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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