The 3 doors
You are in a game show. The host asks shows you 3 doors. He tells you there is $1,000,000 behind one door and in the other 2 doors there was nothing. If you pick the door with the money the. You win it. You pick a door at random. Then the host opens a door and it is empty. Then he asks you if you want to keep your door or change your mind. What should you pick?
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1 solution
This is rather counter intuitive. Your first door has a 1/3 chance of being correct. Then the other 2 doors collectively have 2/3 chance of being correct. Since the host reveals that one of the other 2 doors is empty, then the other remaining door alone has 2/3 chance of it being correct. Hence you should switch.