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?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 1

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.

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