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Topic: Monty Hall Problem< Next Oldest | Next Newest >
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thibodeaux Search for posts by this member.
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PostIcon Posted on: Jul. 20 2013,05:04  Skip to the next post in this topic. Ignore posts   QUOTE
http://en.wikipedia.org/wiki/Monty_Hall_problem

We've probably talked about this before, but I actually sat down and did it with my kids (with cups and a penny). And I realized there's an extremely simple way to explain how it works.

You have a 1 in 3 chance of guessing right. So if you were just playing "guess which door" you'd get it right 33% of the time. We actually did it this way first: I'd hide a penny, and they'd guess.

Then I switched to Monty Hall, but I forced them to always switch their choice. And I realized: you only lose if you actually originally guessed the right one. I.e., you only LOSE 33% of the time.
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Malcolm Search for posts by this member.
I disagree.
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PostIcon Posted on: Jul. 20 2013,09:55 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
Complements.  Like statistical, man.  

I used roughly the same reasoning trying to explain this to non-math folk.  If they're going to get it, they usually get it at the point where I say, "Monty always knows which door has the best prize, so ... "

However, I also know fully grown adults that still refuse to accept that line of reasoning and go with 50%.

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thibodeaux Search for posts by this member.
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PostIcon Posted on: Jul. 20 2013,10:54 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
I've always accepted the Bayesian explanation, but I don't truly "feel" it, if you know what I mean.

This, I get.
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Paul Search for posts by this member.
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PostIcon Posted on: Jul. 22 2013,06:30 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
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Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance.


I can't wrap my head around that for some reason.  Maybe that's why I suck at math.

Let's say they were boxes with a picture of your prize inside.
You pick one and he hands you that box, so there are two left:

1/3 of the time you pick the correct box, and Monty Hall will open either of the remaining boxes.

1/3 of the time you pick the wrong box and Monty Hall must open the box on the left.

1/3 of the time you pick the wrong box and Monty Hall must open the box on the right.

Since 100% of the time you are left with the unopened box in your hand, one other unopened box on stage, and one opened box with a picture of a goat, I just don't see the advantage of switching.

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PostIcon Posted on: Jul. 22 2013,06:40 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
Okay, I see it now.
Since 2/3 of the time he's forced to choose one specific box, 2/3 of the time the remaining box is the winning box.

Weird.

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thibodeaux Search for posts by this member.
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PostIcon Posted on: Jul. 22 2013,06:49 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
I really recommend playing it with your kid. You'll see right away that if you always switch, you will only lose if you actually guessed it right.
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PostIcon Posted on: Jul. 22 2013,06:55 Skip to the previous post in this topic. Skip to the next post in this topic. Ignore posts   QUOTE
I tried posting this afterward but the page times out:

Okay, I see it now.
Since 2/3 of the time he's forced to choose one specific box, 2/3 of the time the remaining box is the winning box.

Weird.

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Malcolm Search for posts by this member.
I disagree.
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PostIcon Posted on: Jul. 22 2013,07:24 Skip to the previous post in this topic.  Ignore posts   QUOTE
Monty always knows which door has the car and he always opens a door to show a goat.

"You know, just to be a dick."

Edited by Malcolm on Jul. 22 2013,07:27

--------------
Diogenes of Sinope:

"It is not that I am mad, it is only that my head is different from yours."

"Other dogs bite only their enemies, whereas I bite also my friends in order to save them."

Arnold Judas Rimmer, BSC, SSC:

"Better dead than smeg."
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