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The 3 Door Problem - 2 Goats, 1 Car


haydon_peter

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Your on a gameshow. You get to the final, and are presented with 3 doors.

Behind one of them, there's a car, while the other two contain goats. Although the show host knows what is behind each door, of course the player does not. After the player makes a first choice, the host opens one of the two other doors, revealing a goat. He then offers the player the option to either stick with the initial choice or switch to the other closed door. Should the player switch?

Get your head round this one people.

"Tic"

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No no. Theres 3 doors. 2 goats, 1 car. No matter which door the contestant initially chooses, there will always be a 'spare' goat for the presenter to reveal.

Oh you just had to piss on my fireworks didn't you. :( But thats jsut my theory, as maybe the presentor would have liked to put the guy out of his misery quicker :lol:

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The probability that the car is behind one of the doors is a third.

When you find out that a goat is behind one of the doors the probability of the car being behind the same door is still one third. The other door now has a two-thirds probability of having a car behind it... So you should switch doors.

Thats the answer to the solution (some poncey twatty public school kid asked me this problem when I was at a university interview, saying it's the kinda stuff that they will ask you...) apparantly... although I still think it's 50-50 myself.

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The probability that the car is behind one of the doors is a third.

When you find out that a goat is behind one of the doors the probability of the car being behind the same door is still one third. The other door now has a two-thirds probability of having a car behind it... So you should switch doors.

Thats the answer to the solution (some poncey twatty public school kid asked me this problem when I was at a university interview, saying it's the kinda stuff that they will ask you...) apparantly... although I still think it's 50-50 myself.

Thats all well and good

so long as you look at the problem from a fixed perspective, of the initial choices.

If you look at it with a real time, moving perspective, the answer changes to 50/50 and the initial choice becomes superfluous, as the second question may as well be which do you want to choose. If you take for instance the usual scenario of a game show, where this choice occurs, the contestant will change their mind a couple of times before they make their final decision one way or the other, therefore making it a 50/50 decision.

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If you draw a tree diagram you'll find that its not a 50/50 chance.

Apparantly some american magazine writer did this in her magazine, had a load of professors and whatnot write in and tell her that she was wrong, and then proved them all wrong.

My electronics teacher couldnt remeber the problem properly, so that kinda ruined it for me :P

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I think that is rubbish, and that:

At first, the chance of picking the car is 1/3.

once a door has been opened the choices are narrowed to 1/2.

no matter what the first chosen door is, the other goat will always be shown, leaving 2 doors, one of which is a car.

Therefore I believe it doesn't matter if the contestant switches as the probability is 50/50.

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I'll try to explain it the way that helped Tic, you have to think hard (Don't reply saying I'm wrong until you have given it at least 10 mins though :( ).

If you picked a goat and you change, you get the car. If you picked the car initially, you get the goat. However, because the chance of picking the car initally is 1/3, chances are that you will have picked a goat (2/3), so you should change.

So you should swap :P

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I'll try to explain it the way that helped Tic, you have to think hard (Don't reply saying I'm wrong until you have given it at least 10 mins though :( ).

If you picked a goat and you change, you get the car.  If you picked the car initially, you get the goat.  However, because the chance of picking the car initally is 1/3, chances are that you will have picked a goat (2/3), so you should change.

So you should swap :P

The thing you said that helped me was:

Chances are, the first time you guess you will be wrong, so changing you mind will help.

"Tic"

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awww bless

if u chose a goat first time *bearing in mind the idea of this is to get the car* then you should defo swap, because you could end up with the same, or a car, so why the feck not go for it?

You don't know if you have a goat or not though. The presenter fellow only shows you one of the doors you didn't choose.

Time to bring out the embarrassed smiley :P

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awww bless

if u chose a goat first time *bearing in mind the idea of this is to get the car* then you should defo swap, because you could end up with the same, or a car, so why the feck not go for it?

I think you've misunderstood!

Right i think i've just got it.

[] < door 1, your 1st choice. Could be a car if you picked this at first (1/3)

[] < door 2, been opened up to reveil a goat.

[] < door 3, if you picked a goat (2/3) this is a car as the host wouldnt open up the car door.

Understand it now! cheers guys

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I think you've misunderstood!

Right i think i've just got it.

[] < door 1, your 1st choice. Could be a car if you picked this at first (1/3)

[] < door 2, been opened up to reveil a goat.

[] < door 3, if you picked a goat (2/3) this is a car as the host wouldnt open up the car door.

Understand it now! cheers guys

I also think you have googled it too! :P I tried last night lol I found a page with near enough the same answer :P

I still don't full understand it though because

[] < door 1 REVEILD TO SHOW A GOAT

[] < door 2 hidden goat

[] < door 3 hidden car

No matter which of the 2 remaining doors you choose, door 1 has allready been reveild so this door no longer exists in the competition. You're origional door, when all 3 doors were shut, you're chance of getting a car was 1/3. Now that one door has been reveiled to show a goat youre chance of getting a car is 1/2. After the first door is reveild to show a goat it leavs yiou with 2 remaining options of which 1 being a car and 1 being a goat, how possible can you look at it in X/3? :P

Edited by Adamm
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