Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#101 2013-04-01 08:24:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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

Offline

#102 2013-04-01 08:33:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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

Here is the formula for Bayes theorem


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#103 2013-04-01 14:27:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#104 2013-04-01 14:57:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#105 2013-04-01 15:11:45

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#106 2013-04-01 15:27:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#107 2013-04-01 18:12:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

#108 2013-04-01 20:53:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#109 2013-04-01 20:58:31

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

Oh yeah!


'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

Offline

#110 2013-04-01 22:29:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#111 2013-04-02 02:07:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

Hi;

For d) i) I am getting:


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#112 2013-04-02 04:33:22

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

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


'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

Offline

#113 2013-04-02 08:19:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#114 2013-04-02 08:21:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#115 2013-04-02 08:25:34

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: rat run probability

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


'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

Offline

#116 2013-04-02 08:28:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#117 2013-04-02 08:36:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#118 2013-04-02 08:41:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#119 2013-04-02 08:50:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: rat run probability

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#120 2013-04-02 08:55:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#121 2013-04-04 05:37:23

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

Re: rat run probability

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."

Offline

#122 2013-04-04 05:47:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

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


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#123 2013-04-04 05:54:18

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

Re: rat run probability

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."

Offline

#124 2013-04-04 05:55:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,248

Re: rat run probability

Hi gAr;

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


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#125 2013-04-04 06:00:25

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

Re: rat run probability

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."

Offline

Board footer

Powered by FluxBB