Riddle #98

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Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?

Answer: Yes, by changing your answer your chances of winning actually goes up from 1/3 to 2/3.

This becomes obvious when expanding the example. Suppose there was 100 doors rather than 3. You pick one and the host shows you that the car is not behind 98 of the doors then asks you to switch to the remaining door or keep the door you picked. Of course you would switch your door because chances are you didn't pick the correct door initially.

For more explanation go to http://en.wikipedia.org/wiki/Monty_Hall_problem#Solutions

Riddle Discussion

By: emiled108 on 20/3/16

Statistically, it changes nothing, odds are 1 in 3, the guy opens the door, odds become 1 in 2 for both doors, changing your pick would only matter if the host would open the doors randomly, lets take the 100 doors example: you pick 1 and the host opens 98 and asks you if you want to change, the odds now become that you picked the right door at first because else, the car would have had 98 in 99 chances to be revealed by the door opening host
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By: gandalf on 29/10/13

Switching the door does matter, the key is that the host of the game show knows more information than you do.
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By: Dani on 28/10/13

Its about the study of Logic, switching the door does not matter, but has a better chance, its complicated
Reply

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