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?

I've always hated this answer. Mathematicians always seem to think this is correct, but never want to try the experiment!

When you eliminate a choice, the state of the puzzle has changed and you have to reconsider it--your previous math is now useless because you interfered with the puzzle and revealed a choice as incorrect!

It's the same puzzle as: You have a quarter. You flip it nine times and it comes up heads each time. What are the odds that the tenth flip will be heads? The answer: 50%. The other tosses are done now.

Same thing here. Once you step in and eliminate a box, it's a new puzzle, and you're simply left with a 50/50 choice. I promise you, if you just get a friend and 3 boxes and try this experiment 200 times, about 100 of them will work out.

Posted by Chris on 2002-05-07 04:50:40