The Student Room Group

Swap The Box?

This is really doing my head in....

A friend sent me this-

Imagine a game show where you had three boxes from which to choose. One box contains the keys to a new car, the other two are empty. You make your choice and the game show host, who knows which box contains the key, opens one of the remaining boxes to show it is empty. He now offers you the swap. Do you stick with the box you have, or do you swap? Does it make any difference? What should you do?


So, is there any more chance of getting the keys if you swap it? Won't say what i think the answer is yet.
Reply 1
I wouldnt mind. Keys to a car were never on my wishlist.

A car on the other hand...:rolleyes:
Lofty
This is really doing my head in....

A friend sent me this-



So, is there any more chance of getting the keys if you swap it? Won't say what i think the answer is yet.
Well it seems if there are only two boxes left (one empty and one with the keys), and the gameshow host has no power over your decision, then it's a 50/50 chance of finding the keys in either of the two remaining boxes. Surely?:confused:
Reply 3
stick to the box you have. better chance then apparently, this is a very common question to come up. shame I can't remember the answer :redface:
Reply 4
Monty Hall problem, it's a very famous problem. You have a 2/3 chance of winning if you switch, but the article explains it better than me.
Reply 5
This is a fairly old problem - you have a better chance if you swap. This is because after picking your first box, the host opens another box, which will always be empty, because he wants you to lose. This gives you a better chance of getting the prize on the box he didn't open. I'm really not explaining this well lol, maybe someone else should try.
Reply 6
wikiwikiwildwildwest
Well it seems if there are only two boxes left (one empty and one with the keys), and the gameshow host has no power over your decision, then it's a 50/50 chance of finding the keys in either of the two remaining boxes. Surely?:confused:


Exactly the logic i was using.

Friend was saying that there is a 2/3 chance you don't have it when you choose the box, so when you swap, you will double the odds from 1/3 to 2/3 (to have it). But there seems to be a gaping hole in that logic.
Reply 7
I'm trying to remember an anlogy a friend told me. He said to think of it as a card game with 13 cards, you're looking for the Ace. After you pick a card the dealer turns over 11 cards all of which are not Aces. Do you switch to the other card turned over?

There is a 12/13 chance that the Ace is one of the cards which you didn't pick, so the other card now has a 12/13 chance of being the Ace, as the probability of your card being the ace is still 1/13.

Once you can visualise it with 13 cards, you can understand why it works with three cards (or doors!)
Reply 8
that'd be a pretty poor gameshow... just opening boxes... god, what kind of loser would come up with a game like that
worldwide
that'd be a pretty poor gameshow... just opening boxes... god, what kind of loser would come up with a game like that
I thought I was the only one who hated 'Deal or No Deal'.:p:
..
(edited 12 years ago)
Reply 11
devilbunny
stick to the box you have. better chance then apparently, this is a very common question to come up. shame I can't remember the answer :redface:

aww well

can't be right all the time :p: