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?

Here is why.  Your odds of being correct initially is 1/3.  Changing your choice does not change the fact that there is still 1 box with a prize and 2 without.

By showing you an incorrect box the odds ARE increased to 1/2 that you will get the prize, (Since now there is 1 box with a prize and 1 without)  but the HOST by showing you an incorrect box is increasing your odds of the prize, not YOU by changing your choice.

Therefore NO, you should not change your choice.

(capitals for emphasis not yelling)

Edited on March 2, 2005, 4:19 pm

Posted by john on 2005-03-02 16:18:09