# 機智問答

如果你在一個電視節目比賽，舞台上擺著3個門，其中一個門後面藏著車，其他的門後面藏著山羊。但你不知道車藏在哪一個門，而且你選擇了其中一個門（假設該門的編號為#1），但在你選擇後，門沒有立刻開啟，反而是知道答案的主持人把其中一個門，不是你剛剛選擇的門（#3）打開，門後面出來了山羊。然後主持人問了你，剩下兩個門，你要換你的選擇嗎（從#1換到#2）？真正的機智問題是，這時切換原先的選擇，將#1換到#2門，得到車子的機會會提高嗎？還是不變？

Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?