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#1 2014-10-29 23:32:43

oem7110
Member
Registered: 2010-12-08
Posts: 24

Is Monty Hall problem still recognized to be corrected?

Monty Hall problem
http://mathforum.org/dr.math/faq/faq.monty.hall.html

  1) You make an initial guess.

  2) You're told:  In a moment, Monty is going to show you
     a goat behind one of the other doors.
     When he does that, will you want to switch to the
     remaining door, or not?
     You have to answer now.

  3) You decide whether to switch or not.

  4) Monty shows you a goat.

  5) You switch or not, as you decided in step 3.

Questions:
1) Initial choice : "2/3" probability of initially selecting a goat.
   This is clear with no problem.

2) Before opening any door with 3 unopened doors available for
   selection, the probability of initial choice is still valid at
   this moment.
   
   After opening a door by Monty and only 2 unopened doors available
   for selection.  The problem is starting here on calculating
   probability for second choice.

3) Second choice : how does the probability of second choice depends
   on the initial choice? Making second choice is after initial
   choice in this order, but it does not make any depended condition
   on calculating probability for second choice. Both choices are
   independent to each other, there is missing connection on how to
   both choices related to each other mathematically.

Does anyone have any suggestions?
Thanks in advance for any suggestions

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#2 2014-10-30 00:12:31

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Is Monty Hall problem still recognized to be corrected?

The 2/3 - 1/3 results can be obtained experimentally


'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'
I'm not crazy, my mother had me tested.

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#3 2014-10-30 00:27:40

oem7110
Member
Registered: 2010-12-08
Posts: 24

Re: Is Monty Hall problem still recognized to be corrected?

This is the question related to this topic...

Second choice : how does the probability of second choice depends
   on the initial choice? Making second choice is after initial
   choice in this order, but it does not make any depended condition
   on calculating probability for second choice. Both choices are
   independent to each other, there is missing connection on how to
   both choices related to each other mathematically.

Do you have any suggestions?
Thanks in advance for any suggestions

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#4 2014-10-30 01:12:29

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Is Monty Hall problem still recognized to be corrected?

Do you know prior and posterior probability distribution are? Are you familiar with 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'
I'm not crazy, my mother had me tested.

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#5 2014-10-30 01:26:42

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Is Monty Hall problem still recognized to be corrected?

Monty Hall?  That means Christmas must be coming.  For like Santa, Monty surfaces once a year.  smile

hi oem7110

What didn't you like about the mathforum explanations?

Here's my suggestion:  Take a look at some past threads:


http://www.mathisfunforum.com/viewtopic.php?id=8978

http://www.mathisfunforum.com/viewtopic.php?id=15598 from post 12 on.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2014-10-30 02:08:11

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Is Monty Hall problem still recognized to be corrected?

Did you know that there is a full [website](http://montyhallproblem.com/) about it?

QKm8oUg.png


'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'
I'm not crazy, my mother had me tested.

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#7 2014-10-30 03:35:23

oem7110
Member
Registered: 2010-12-08
Posts: 24

Re: Is Monty Hall problem still recognized to be corrected?

1) After Monty opens a door with goat, am I still able to switch my
initial choice into this opened door with goat? It may sound stupid to
pick an opened door with goat instead of 2 unopened doors, but it
could be the condition under Monty Hall Problem.

2) After Monty opens a door with goat, I cannot switch my initial
choice into this opened door with goat.

I would like to confirm which one is correct condition under Monty
Hall Problem.

Does anyone have any suggestions?
Thanks, to everyone very much for any suggestions :>

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#8 2014-10-30 03:39:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Is Monty Hall problem still recognized to be corrected?

Hi;

1)? Why would you pick a door that has a goat for sure? You always have to pick an unopened door.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2014-10-30 03:40:28

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Is Monty Hall problem still recognized to be corrected?

I believe that it is assumed you would not choose the door that had been revealed as having a goat.  So interpretation (2) is correct.

Bob

whoops.  hi bobbym.  You got there first.  smile


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#10 2014-10-30 04:01:28

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Is Monty Hall problem still recognized to be corrected?

After Monty opens a door with goat, if I am still able to switch my initial choice into this opened door with goat.

No, that is not allowed.


'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'
I'm not crazy, my mother had me tested.

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#11 2014-10-30 04:13:05

oem7110
Member
Registered: 2010-12-08
Posts: 24

Re: Is Monty Hall problem still recognized to be corrected?

Agnishom wrote:

After Monty opens a door with goat, if I am still able to switch my initial choice into this opened door with goat.

No, that is not allowed.

If Monty claimed that opened door with goat is not allowed to be selected, for the second choice, there is only 2 doors available for selection (Switch or Stay). "1/2" chance to get the CAR is closer to probability in practice instead of "2/3"

Therefore, I assume that the opened door with goat is still considered as a choice for selection in order to calculate "2/3" probability in Monty Hall Problem, if this is the case, then everything is much clear on probability calculation.

On the other words, in reality, you would never select the opened door with goat, but in Monty Hall Problem, Monty still considers this opened door with goat as a valid choice for selection under Monty Hall Problem.

Do you 100% confirm that selecting the opened door with goat is not allowed under Monty Hall Problem?

Thanks, to everyone very much for any suggestions :>

Last edited by oem7110 (2014-10-30 04:20:53)

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#12 2014-10-30 04:21:13

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: Is Monty Hall problem still recognized to be corrected?

"1/2" chance to get the CAR is closer to probability in practice instead of "2/3"

No!  These two events (car or goat) are NOT equally likely.  Have you looked at all the analysis ?

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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