rat run probability

anonimnystefy · 2013-04-01 08:24:04

You were going to do Bayes' theorem.

bobbym · 2013-04-01 08:33:12

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

Here is the formula for Bayes theorem

Agnishom · 2013-04-01 14:27:15

What does the notation

mean?

anonimnystefy · 2013-04-01 14:57:25

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

Agnishom · 2013-04-01 15:11:45

Got it from the wiki,
Thank You

bobbym · 2013-04-01 15:27:57

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.

Agnishom · 2013-04-01 18:12:42

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

bobbym · 2013-04-01 20:53:25

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.

Agnishom · 2013-04-01 20:58:31

Oh yeah!

anonimnystefy · 2013-04-01 22:29:59

Hi Agnishom

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

bobbym · 2013-04-02 02:07:34

Hi;

For d) i) I am getting:

Agnishom · 2013-04-02 04:33:22

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

anonimnystefy · 2013-04-02 08:19:43

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?

bobbym · 2013-04-02 08:21:39

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.

Agnishom · 2013-04-02 08:25:34

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

bobbym · 2013-04-02 08:28:42

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.

anonimnystefy · 2013-04-02 08:36:34

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

bobbym · 2013-04-02 08:41:49

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.

anonimnystefy · 2013-04-02 08:50:33

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.

bobbym · 2013-04-02 08:55:44

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.

gAr · 2013-04-04 05:37:23

I'm getting 7 / 16 for (ii)

bobbym · 2013-04-04 05:47:14

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

gAr · 2013-04-04 05:54:18

Okay, verify when you are done.

bobbym · 2013-04-04 05:55:59

Hi gAr;

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

gAr · 2013-04-04 06:00:25

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)

Math Is Fun Forum

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

Re: rat run probability

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

Re: rat run probability

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

Re: rat run probability

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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