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?
You will have a fifty-fifty chance regardless of which box you pick first, because after you pick, you are already shown that you did not pick one of the two incorrect boxes--therefore, you either do or don't have the correct box, and have a 50% chance of having the correct box, whether you guessed correctlt the first time or not.
Solution
