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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts No Subject | Comment 18 of 42 |
I don't think you should change your selection because the boxes are independent of each other .  However, your chances do increase, but they don't increase because you suddenly decide to pick up the other box.  Example: You first select box A.  Because there are 3 boxes total, you have 1/3 chance of winning, and 2/3 chance of losing.  Then box C is shown to be empty.  Suddenly there are only two boxes (A and B) that have a possible winning.  Thus, you now have 1/2 chance of winning and a 1/2 of losing.  These odds will not increase if you decide to select box B instead of A, for there are still two boxes, each possible of yielding a win.

Edited on May 2, 2004, 8:59 pm
  Posted by logischer Verstand on 2004-05-02 20:53:08

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