Monty Hall Problem

[Anonymous]

If you haven't heard of this, then don't Google it - just read through it and see if you follow

If you are on a game show, and there are 3 doors; A, B and C. I tell you that  afancy sports car is behind one of the doors, and behind the other two is nothing, which door would you pick?

Now, if I tell you that the door to the right of your chosen door (or the far left, if you chose the far right) hasnothing behind it, that means that only your door and one other are unknown. Do you wish to keep your original door or switch for the other door?

[perksie]

You switch.

I'm not sure how it works but I think it gives you a slight advantage.

[MI5]

Statistically at the start you have a 1 in 3 chance of getting the correct door. If you stay with the same door the odds remain at 1 in 3. If you switch doors your odds increase to 1 in 2. Therefore you are 1/3rd more likely to win.

To put it another way, staying with the same door gives you a 33% chance of winning, but switching gives you a 66% chance of winning

[Anonymous]

Ok, assuming A,B & C are the same size door, They go left from right.

I chose B, So therefore C is empty.

That leaves A & B. You stated that the box to the right (Or far left if you chose C) is empty.

So If you chose C, A is empty
If you chose B, C is empty
if you chose A, B is empty

So where is the car???

(God, I hope I don't look a pillock!)

[Anonymous]

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@Anonymous wrote:
Ok, assuming A,B & C are the same size door, They go left from right.

I chose B, So therefore C is empty.

That leaves A & B. You stated that the box to the right (Or far left if you chose C) is empty.

So If you chose C, A is empty
If you chose B, C is empty
if you chose A, B is empty

So where is the car???

(God, I hope I don't look a pillock!)

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They aren't all empty, it's just to simplify a specific example.

So if you pick any box (say B as you said) and I tell you C is empty so the car is either behind door A or door B, you have a chance to switch your door before opening it or you can stay with your original choice. What do you choose and why?

And what are the odds of it being behind door A or B?

[Anonymous]

I'd stay with my original choice as I've been told a variable about that choice and not the switch.

Surely the odds are now reduced to 50/50?

[MI5]

No its not 50/50. You had 3 variable to start with so the odds of it been behind your door are still 1 in 3.

[Anonymous]

The odds are still 1/3 but the odds of you finding is now 50/50

[Anonymous]

Now putting my theory into words after reading MI5 evaluation.

I get that by switching there is now a 2/3 chance of finding the car.

[EDIT] Even though I don't know why!

But, yes I would switch.

Off to Google this now! Very good question!

[perksie]

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@MI5 wrote:

Statistically at the start you have a 1 in 3 chance of getting the correct door. If you stay with the same door the odds remain at 1 in 3. If you switch doors your odds increase to 1 in 2. Therefore you are 1/3rd more likely to win.

To put it another way, staying with the same door gives you a 33% chance of winning, but switching gives you a 66% chance of winning

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That's the best and simplest explanation of how it works, at least to my battered brain.

A load more theories here, including the James May 100 sample test:

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