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?
posted solution aside, the answer to the problem depends on some "rules" that are not contained in the problem. For example, if the actual rules are that a box at random will (always) be opened and shown (but in this case happens to be empty), then changing your selection would have no impact on your odds. If the rules state that an empty box is shown, then you double your chances. This would lead you to change your choice, as you could end up increasing your odds, but not decreasing your odds. ---However---, if the box is chosen by a cunning person, who also has the option of not showing a box, then it isn't necessarily in your favor. The "host" could play on your grasp of the probabilities and offer a change more often when the prize is (already)chosen than not, which would lower your chances of winning the prize.
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