3 boxes You are playing a game. A person (game host) shows you 3 boxes. 1 box contains $100, 2 others are empty. You need to choose one of the boxes. If the box you chosen contains money you win.
Peter
That's an easy one! The probability that the first box is the $100 box is 1/3 (there are three boxes); just like the other two boxes.
Bart Willems
This is the same os the Monty Hall question. I disagree with the previous poster's response (2/3) as will as most other that have respond to that problem.
Steve B.
Ho Hum.
David Clayworth
David, then explain to me why one random choice has different odds than another random choice when your pool of available choices are the same.
Steve B.
Another way to look at all this...
Steve B.
Did you read the previous discussion, Steve?
David Clayworth
The real question here... have you read my posts at all?
Steve B.
David... one other thing I noticed in your post, thus furthering my cause...
Steve B.
I read your posts in detail. You're not the first person to argue like this. Read the web sites I linked to.
David Clayworth
Steve, suppose that the game host did not give you the chance to switch--he just opens the box you chose. I think we would both agree that the probability of winning in this case is 1/3.
Peter Meilstrup
Steve, I think it becomes more obvious when there are more doors, as you said.
luv2puz
well, that seems to be very confusing..I have only one point to say..
amit
Sampling without replacement.
Lenko Donchev
This is a fascinating problem, isn't it? Something about it seems to challenge all our preconceptions about how probability works.
David Clayworth
let me try to take a stab at why i think 2/3 (and hence switching) is the right answer.
Amit
David,
Lenko Donchev
The problem with most of these posts is the commets that sez "what if this, or what if that".
Steve B.
Let me ask this question...
Steve B.
Steve:
a2800276
Not sure if I understand the logic behind the card comparison.
Steve B.
The card comparison is simple: you try to pick a prespecified card (the door with the prize behind it). Once you've made your pick, I (Monty) get to select which cards to show you (which doors to reveal), basically sorting out all non-winning cards (showing you the doors which don't conceal the prize). I keep one card, which is either (a) the winning card or (b) if you have picked correctly on your initial guess, a random card.
a2800276
Wow... amazing how these things get dragged out...
Giles
This is one problem that really made steam come out my ears. At first I thought that switching made no difference. It would always be a 50/50 chance. Then after reading more and more of the replies, I feel that switching will give you a better chance. I conducted some tests from one of the links supplied by David.
Tim Mok
The important point is, when Monty opens one of the boxes you didn't pick, he is specifically opening one of the empty ones. Therefore, Monty's choice does not involve any odds.
James R. Manka
Its really an interesting discussion... After reading all the posts i feel that i agree with Steeve.
Joseph
Well, after thinking a little further i feel that swithicng will be a better idea... I can give you a more clear argument in its favour as follows.
Joseph
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