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

You are not logged in.

## #76 2013-04-01 23:02:31

Agnishom
Real Member

Offline

### 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'
'Who are you to judge everything?' -Alokananda

## #77 2013-04-01 23:09:52

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #78 2013-04-01 23:11:40

Agnishom
Real Member

Offline

### 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'
'Who are you to judge everything?' -Alokananda

## #79 2013-04-01 23:17:38

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #80 2013-04-01 23:20:07

anonimnystefy
Real Member

Offline

### Re: rat run probability

You also need the solution to b).

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #81 2013-04-01 23:22:45

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #82 2013-04-01 23:26:32

anonimnystefy
Real Member

Offline

### 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?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #83 2013-04-01 23:29:57

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #84 2013-04-01 23:34:02

anonimnystefy
Real Member

Offline

### 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).

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #85 2013-04-01 23:40:01

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #86 2013-04-01 23:55:05

anonimnystefy
Real Member

Offline

### Re: rat run probability

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #87 2013-04-02 00:01:08

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #88 2013-04-02 00:03:35

anonimnystefy
Real Member

Offline

### Re: rat run probability

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #89 2013-04-02 00:07:59

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #90 2013-04-02 00:09:20

anonimnystefy
Real Member

Offline

### Re: rat run probability

I bigger one (10 million tries) gave 0.246225.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #91 2013-04-02 00:11:28

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #92 2013-04-02 00:13:08

anonimnystefy
Real Member

Offline

### Re: rat run probability

How?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #93 2013-04-02 00:19:18

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #94 2013-04-02 00:24:01

anonimnystefy
Real Member

Offline

### Re: rat run probability

Why is that?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #95 2013-04-02 00:26:56

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #96 2013-04-02 00:32:00

anonimnystefy
Real Member

Offline

### Re: rat run probability

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #97 2013-04-02 00:38:44

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #98 2013-04-02 01:30:57

anonimnystefy
Real Member

Offline

### Re: rat run probability

Okay. Post if you get anything...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #99 2013-04-02 05:43:20

Agnishom
Real Member

Offline

### 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'
'Who are you to judge everything?' -Alokananda

## #100 2013-04-02 07:15:47

bobbym
Administrator

Offline

### 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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## Board footer

Powered by FluxBB