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## #1 2014-04-25 11:08:27

ManiticMath
Member
Registered: 2014-04-24
Posts: 29

### Monty Hall puzzle

I must protest the answer they gave for the Monty hall puzzle. The puzzle is as follows.

Puzzle:
The host, Monty Hall, offers you a choice of three doors. Behind one is a sports car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).
Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.
You cannot hear the goats from behind the doors, or in any way know which door has the prize.
Should you stay, or switch, or doesn't it matter?

The answer they gave is as follows.

Your first choice has a 1/3 chance of having the car, and that does not change.
The other two doors HAD a combined chance of 2/3, but now a Goat has been revealed behind one, all the 2/3 chance is with the other door.
You better switch!
(Unless you really want a goat)

I don't understand how they got there to be a 2/3 chance for the other door.
When you start out, you have a 2/3 chance of picking a goat, and a 1/3 chance of picking a car. You then pick a door, and then one of the doors with a goat is revealed. This now means that there is 1 door with a car behind it, and 1 door with a goat behind it. There should be a 50:50 chance for the car and the goat. So either the puzzle answer is wrong, or there is some part of probability that I don't know about.Can someone explain why the answer put 2/3 of the chance of the car on the other door?

When ever I see a brand new new math problem, I want to solve it. Then I want to burn it. Then I want to rebuild it in a new, more streamlined way.

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## #2 2014-04-25 11:33:08

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

Hi;

It is definitely favorable to switch as long as you know that Monty knows where the car is.

The problem first appeared over here in Vegas in Parade magazine in the early 90's and was correctly solved by Marilyn Vos Savant, reputedly the highest IQ in the world.

Immediately math professors attacked her but she remained steadfast and eventually proved she was right. Unbeknownst to them this all appeared in a statistics journal in 1959 and all she had to do was cite the article.

Here are some solutions on this forum.

http://www.mathisfunforum.com/viewtopic … 20#p175920

http://en.wikipedia.org/wiki/Monty_Hall_problem

If you can not get them I have posted Marilyn's solution which I still think is the best one.

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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## #3 2014-04-25 11:59:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,201
Website

### Re: Monty Hall puzzle

I remember experimentally verifying that it is indeed 2/3. Should I post 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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## #4 2014-04-25 12:01:37

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

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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## #5 2014-04-25 12:06:10

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,201
Website

### Re: Monty Hall puzzle

Agnishom wrote:

'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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## #6 2014-04-25 12:27:28

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

Here is the MVS whole article as it appeared in Las Vegas in 1991.

http://marilynvossavant.com/game-show-problem/

Notice how cleverly Marilyn does not mention the earlier articles that she probably copied from. The hallmark of true genius!

Albert Einstein wrote:

Creativity is knowing how to hide your sources.

Fame too!

bobbym wrote:

If you can not get them I have posted Marilyn's solution which I still think is the best one.

I used to think it was the best solution but now since I am now an experimental math type I like Agnishom's solution best!

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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## #7 2014-04-25 12:35:23

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,201
Website

### Re: Monty Hall puzzle

Thank you but mine is just verification not a solution.

'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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## #8 2014-04-25 13:01:18

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

it was the only one that convinced the great Paul Erdos and the reppies at Los Alamos. A simulation is very strong.

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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## #9 2014-04-25 13:08:43

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 20,201
Website

### Re: Monty Hall puzzle

It is for believing

'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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## #10 2014-04-25 13:12:04

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

Supposing I am working on a gAr super tough problem. If my gf or series or recurrence or any other math kaboobly doo does not agree with my simulation, I throw the math away knowing the simulation is right and the math is wrong.

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

## #11 2014-04-25 23:32:38

ManiticMath
Member
Registered: 2014-04-24
Posts: 29

### Re: Monty Hall puzzle

Ok. I understand now.... Thanks for showing me why. I see why the answer you  guys gave was right, but please make the answer explain more.

When ever I see a brand new new math problem, I want to solve it. Then I want to burn it. Then I want to rebuild it in a new, more streamlined way.

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## #12 2014-04-26 01:10:58

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

Did you tree it as Marilyn did?

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

## #13 2014-04-26 10:44:20

ManiticMath
Member
Registered: 2014-04-24
Posts: 29

### Re: Monty Hall puzzle

yep.

When ever I see a brand new new math problem, I want to solve it. Then I want to burn it. Then I want to rebuild it in a new, more streamlined way.

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## #14 2014-04-26 21:21:42

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

I have one more explanation from the original stats journal would that help?

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

## #15 2014-04-27 00:28:28

ManiticMath
Member
Registered: 2014-04-24
Posts: 29

### Re: Monty Hall puzzle

Yes. I think it would.

When ever I see a brand new new math problem, I want to solve it. Then I want to burn it. Then I want to rebuild it in a new, more streamlined way.

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## #16 2014-04-27 05:21:25

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,650

### Re: Monty Hall puzzle

Hi;

If he switches he wins 6 times out of 9 possibilities. If he does not he wins 3 out of 9 possibilities.

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