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#26 2013-04-06 02:02:23

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: Bayes' theorem problem

Got it,
Thanks bobbyM and gAr

So after all this isn't related to Bayes'?


'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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#27 2013-04-06 02:03:38

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

Why do you say that?


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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#28 2013-04-06 02:05:36

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: Bayes' theorem problem

Because I don't see where you use it


'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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#29 2013-04-06 02:08:37

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

Re: Bayes' theorem problem

Hi Agnishom,

It is related to Bayes', we just didn't write a formula for that!


"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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#30 2013-04-06 02:09:59

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

There is a formula that covers what he did, it is called the extended form of Bayes theorem.


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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#31 2013-04-06 02:21:45

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

I tried to match that too.

p(a|b) = (p(b|a)*p(a))/((p(b|a)*p(a))+(p(b|not a)*p(not a))


'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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#32 2013-04-06 02:28:35

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

What you wrote is the extended form:

That has the form of his answer. That is what I was working on, trying to fill that in but I must have missed something.

His use of the tree is better, it lends itself to computation better.


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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#33 2013-04-06 02:38:10

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Surely thats better.

But how do you use that formula?


'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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#34 2013-04-06 02:39:48

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

Re: Bayes' theorem problem

I thought of something like:

and we have


"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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#35 2013-04-06 02:41:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

Hi;

Look at his answer:

then look at the formula:

try replacing corresponding parts.

I did not see gAr's answer until I posted. He got the solution so he is the guy to ask.


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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#36 2013-04-06 02:57:29

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Now in that part, what does A and B stand for?


'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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#37 2013-04-06 03:01:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

Hi Agnishom;

You are forgetting that I did not get the answer so I must not have filled that formula in correctly.


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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#38 2013-04-06 03:04:45

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Okay, I am contended with the tree anyway. Next time I will think of one


'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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#39 2013-04-06 03:06:19

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

gAr wrote:

I thought of something like:

and we have

Yes, yes, it seems more clear but how does it fit into the formula?

I mean how do you relate the calculation with it?

Last edited by Agnishom (2013-04-06 03:07:09)


'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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#40 2013-04-06 03:15:00

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

Re: Bayes' theorem problem

Hi,


You can plug in the values now..


"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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#41 2013-04-06 03:24:22

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Okay! Thanks


'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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#42 2013-04-06 03:47:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

Hi;

I found a couple of pages that agree with his approach and also calculate the number for you.


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

#43 2013-04-06 03:49:12

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Webpages?


'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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#44 2013-04-06 03:50:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem

Hi;

Yes, websites. Have not gone over them completely so I do not know how good their computations are.


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

#45 2013-04-06 03:54:10

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

May I have the link?


'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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#46 2013-04-06 04:07:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: Bayes' theorem problem


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

#47 2014-10-04 19:19:34

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

A bag contains 5 balls. Two balls are drawn and are found to be white.

What is the probability that all the balls are white?


'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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#48 2014-10-05 06:56:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,536

Re: Bayes' theorem problem

Insufficient information for a solution.  You might as well ask, if I draw two whites what is the probability that the next person to knock on my door has no trousers on.

It isn't a Bayes problem, as there are not two events.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#49 2014-10-05 07:01:20

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

That is what I suspected. smile

Let me show you the solution and please tell me if you can digest it.


'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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#50 2014-10-05 07:06:02

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Bayes' theorem problem

Sandeep wrote:

PIf P(A)=probability of getting the bag chosen for drawing balls when all the 5 balls in the bag are white.

P(B)=probability of getting the bag chosen for drawing balls when  only 4 balls in the bag are white

P(C)=probability of getting the bag chosen for drawing balls when only 3 balls in the bag are white

P(D)=probability of getting the bag chosen for drawing balls when only 2 balls in the bag are white

P(E)=probability of getting two white balls drawn from the bag

P(E/A)=probability of two white balls drawn when the bag is chosen which has all white balls in it

P(E/B)=probability of two white balls drawn when the bag is chosen which has only 4 white balls in it

P(E/C)=probability of two white balls drawn when the bag is chosen which has only 3 white balls in it

P(E/D)=probability of two white balls drawn when the bag is chosen which has only 2 white balls in it.

So using baye's theorem

required probability


   
   

     

Last edited by Agnishom (2014-10-05 07:07:52)


'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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