Monty Hall Problem

Anything you want to talk about.

Is it to your advantage to switch your choice?

Your odds of winning are increased by switching.
38
76%
Your odds of winning are increased by keeping your original choice.
3
6%
Your odds of winning are the same (50/50) whether you switch or not.
9
18%
 
Total votes : 50

Monty Hall Problem

Postby Tarsier » 15 Nov 2017, 17:45

The Monty Hall probability problem is nothing new. Many of you have probably encountered it. However, I was talking about it with one of our junior high classes and enjoyed the debate. If you haven't encountered it, the problem appears below, so please don't look it up - try to reason and comment based on your own analysis. The fun in the problem is less trying to figure it out, and more watching the firm determination on both sides of the argument. It's like watching people argue about color of a dress, only with the Monty Hall problem, a real answer does exist.

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

I've attached a poll to summarize any responses.

In this same thread, if anyone has suggestions of other fun probability puzzles, I'd love to have links or descriptions.
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Re: Monty Hall Problem

Postby mjparrett » 15 Nov 2017, 17:58

Ah the black/blue dress! Anyone that tells me otherwise is lying!!

I always thought you should swap. And I assume there is mathematical logic behind it (i.e. your original choice was a 1/3 guess but now the other door is 1/2?) But that sounds mad. And considering my previous forum post I am clearly not good enough at Maths to know the official answer!
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Re: Monty Hall Problem

Postby Don Juan of Austria » 15 Nov 2017, 18:03

Confusing poll, that. . . and definately a white and gold dress. ;)
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Re: Monty Hall Problem

Postby jimbobicus » 15 Nov 2017, 18:07

This one is a classic. I won't say anything to spoil it for others. Although to clarify the problem... regardless of what door the contestant chooses, the game show host will always show you that behind one of the other 2 doors is a goat. The host can always do this because 2 doors have goats behind them.
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Re: Monty Hall Problem

Postby Willie900 » 15 Nov 2017, 18:10

My answer in spoilers. At risk of sounding cocky, this problem has as definite an answer as 1+1 (it is math, after all!) so I'm sure this is the right one.
You always want to switch.

Imagine a similar game show, but instead of three doors there are one hundred doors, one of which has a Ferrari behind it, the other ninety-nine have goats. You pick a door at random, and the announcer opens ninety-eight doors, which all have goats, and leaves one door still closed.

You'd be mad not to switch!

The regular Monty Hall Problem is the same thing on a smaller scale.

If you're not convinced that the problem scales in this way, let me just show how the regular problem works.

You pick one of three doors. The chance that that door has a car behind it is 1/3. Therefore the chance that the car is behind one of the other two doors is 2/3.

When the announcer opens one of the doors you didn't choose, showing a goat, the odds haven't changed--the chance the door you chose has a car is still 1/3, and the chance one of the other two doors has a car is still 2/3--except now you know which of the other two doors has a 2/3 chance of having a car. So now you have a door that you chose, with a 1/3 chance of having a car, and the other door has a 2/3 chance of having a car--unless you're dying to have a pet goat, you should definitely switch your choice!
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Re: Monty Hall Problem

Postby Tarsier » 15 Nov 2017, 18:11

Don Juan of Austria wrote:Confusing poll, that. . . and definately a white and gold dress. ;)


The poll is confusing? Or the puzzle? I'm not sure how I could have made the poll more clear, but open to suggestions.
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Re: Monty Hall Problem

Postby Tarsier » 15 Nov 2017, 18:16

Willie900 wrote:My answer in spoilers. At risk of sounding cocky, this problem has as definite an answer as 1+1 (it is math, after all!) so I'm sure this is the right one.


Hah! Willie's spoiler makes a great point. I suppose the answer depends on whether you want to win the car. Some of you might prefer the goat!

Let's assume the goal is to win a car (even if you hate cutting grass!).
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Re: Monty Hall Problem

Postby Willie900 » 15 Nov 2017, 18:22

Tarsier wrote:
Willie900 wrote:My answer in spoilers. At risk of sounding cocky, this problem has as definite an answer as 1+1 (it is math, after all!) so I'm sure this is the right one.


Hah! Willie's spoiler makes a great point. I suppose the answer depends on whether you want to win the car. Some of you might prefer the goat!

Let's assume the goal is to win a car (even if you hate cutting grass!).

Goats are adorable
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Re: Monty Hall Problem

Postby jay65536 » 15 Nov 2017, 18:38

Here is an even better question than the one in the spoiler, to help you see what the right answer is.

What is the chance that Door No. 1 has a goat behind it?
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Re: Monty Hall Problem

Postby Tarsier » 15 Nov 2017, 18:45

jay65536 wrote:Here is an even better question than the one in the spoiler, to help you see what the right answer is.

What is the chance that Door No. 1 has a goat behind it?


It's only better in that it provides a hint. The question in the OP was better in that it creates fun arguments (though not here yet).
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