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Pick a box! (Posted on 2002-03-28) Difficulty: 3 of 5
You are shown three boxes, and told that one of them contains a prize. You are then asked to pick one box, and if that box is the one with the prize, you will win it. After picking a box, you are shown that one of the other two boxes is empty, and offered a chance to change your selection.

Should you do this? Would changing your choice to the other remaining box affect your odds of winning? Why or why not?

See The Solution Submitted by levik    
Rating: 4.2857 (14 votes)

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50% is the ONLY answer. | Comment 6 of 42 |
Once one box has been eliminated, there are only TWO boxes to choose from. The only way the odds could be 2/3 is if you got to get whatever was under BOTH of the remaining boxes, but you only get one.

[a] [b] [c] ...picking A, then C is removed.

The puzzle is now a decision between A and B. There is no C, it has been removed. If you wanted to be dumb, you could still say box C was still in the game and just KNOW that it was empty, so you would obviously not choose it because it is a certain loss. This leaves the only two REAL options between A and B--a 50% chance.
  Posted by Mike on 2002-05-10 15:32:06
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