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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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Some Thoughts Come on guys! | Comment 12 of 42 |
This one is easy, it all depends on whether you change your answer or not!



Think about it, if you stay the same there is *still* a one and three chance that you will have the right answer, because you chose the box *before* you were told one of the empty ones.



The bit which changes is if you change your descision, look at it on a tree diagram.

You have a one in three chance of getting the prize, right? So if you change, there is one in three chance that you will change from the prize to an empty box, in other words a two in three chance you will get a prize. That is why, when playing this game, always change your descision after one of the empty boxes is revealed. If you still don't understand draw the three boxes and mark one "P" then take each one in turn revealing on box and changing, two out of the three times you will get the prize.



Arcus...
  Posted by Arcus on 2002-10-29 09:25:40
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