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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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Agree with solution? Problem simplified? | Comment 35 of 42 |

OK, looking some things over.

Let's simplify the problem for those who still do not seem to get it (i.e. ME! Maybe others.)

You are shown a legal coin, and told that the host will flip the coin, and if you guess correctly you will get a prize.  After flipping the coin, you are shown that the inverse of the coin is the guess that you made. (This does not directly show you that the choice you made is wrong. I believe this follows the intent of the original problem.) You are then given a chance to change your guess.  Should you change your guess. 

Of course you should, lowercase john!

Does this follow the intent of the original problem and support the solutiuon?  I believe it does.  Now allow me to re(-?)examine some of my earlier posts.  I believe most of my conclusions will be correct but will not apply to the problem for some reason. 

  Posted by john on 2005-03-07 17:11:43
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