Three Doors Puzzle (& Other Conundrums)

[Chris_D]

You're in a game show, and the host explains to you the following:

In front of you are three doors. Behind one is a brand new car, and behind the others is the booby prize, a goat. You need to pick a door - 1, 2 or 3. Which ever door you pick, I will open one of the doors with a goat behind it. I will then ask you whether you want to keep the door you chose, or change to the other remaining door. If your final choice is the door with the car, you win the car. Otherwise, you lose.

You go ahead and pick a door (lets say, for example, you pick door 1). The gameshow host opens a different door - lets say door number 3 - revealing a goat. The host now asks you whether you would like to stay with Door 1, or change your selection to Door 2.

Are you better off changing to door 2?

(note that this isn't a trick question, there is no playing on words or trickery, it's straight forward)

[pb]

Yes. Open door 2.

[lubie]

but door 1 is a better colour

[pissface]

always choose another door. it improves the odds

[DropKick]

I wouldve thought the goat was the better prize.

[pissface]

I wouldve thought the goat was the better prize.

apparently it has boobies !!!

[Henry Dorset Case]

uhhhhhhh

say the doors are:

a = goat

b = car

c = goat.

I say open door A and door C is opened. I know that whatever door is opened will have a goat behind it. I therefore know that whatever I choose, I have a one in two chance of getting the goat at Q2.

therefore it makes no difference whether I change my inital answer or not, surely?

If it was distraction, you'd have to be milking the goat to get the chance to answer the question. thatd be cool

[lubie]

can't be arsed today either, huh?

[Natral]

I love that show

And yeah, your options are now exactly 50/50, no?

[Henry Dorset Case]

milk that goat!!

[happybaboon]

I think it's called the Monty Hall problem. I remember something about it in one of those university things I did once

I drewd a picture that might help you understand HDC. It shows that you've got a 2/3 chance of winnz0ring if you change your selection.

[psychavoc]

And yeah, your options are now exactly 50/50, no?

That's what I thought

Out of the three doors, you only know the contents of one of them (the one with the goat). So either the door you've originally picked or the other door contains the prize.

[pissface]

also, the first time yu made you choice, the door you chose had a 1/3 chance of being correct. the second time, of the two doors, the other one now has a 1/2 chance

[wgtngrl]

Are you better off changing to door 2?

No. No matter which door you chose first, technically you had a 50/50 chance of choosing the car.

It's logical to think you had a one in 3 chance of getting it right first time but no matter what you choose they're going to remove one wrong answer. It's effectively the same as only having 2 doors to chose from, one with car, one with goat. And that's what you're left with.

As long as the car stay's where it is, you still have a 50/50 chance of getting it.

If you win the car, do you get the goats as well?

[Henry Dorset Case]

can't be arsed today either, huh?

I think everyone is starting to notice.....