time to change?

heavenarch · 发表于 2005-3-11 17:14:20

在一电视节目中，一候选人可在三扇门中任选一扇，但仅在一扇门后有一辆汽车（奖品），其余为空。选完后，主持人会打开另两扇门中门后为空的一扇。现在该候选人可选择另一扇门，或坚持原选择。问如何赢得汽车的可能性大些？

第一次发贴帮主就推荐，仲算给面了。感觉这里数学的东西太多了，找了个好玩的题目。

新用户 · 发表于 2005-3-11 19:36:35

这提在各大网站的论坛有过很激烈的争论，这是一道很有意思的概率题，我想这里绝大多数人一定熟悉此题。

以前没有见过此题的朋友，值得花时间想一想。

最后说明一点，我认为有一个条件很重要，就是：主持人事先知道奖品在哪一扇门后面（如果主持人事先不知道，结果就会不同？）。

>> 第一次发贴帮主就推荐，仲算给面了。感觉这里数学的东西太多了，找了个好玩的题目。

你的那到推荐题目，我认为非常好，所以推荐。
你来这里出题，解题就是很给我面子

yma16 · 发表于 2005-3-11 22:37:11

>>最后说明一点，我认为有一个条件很重要，就是：主持人事先知道奖品在哪一扇门后面...

Why do you think so? I disagree.

怀疑 · 发表于 2005-3-11 23:57:12

The host just needs to make sure that the door that she opens does not have a car.

ob · 发表于 2005-3-12 04:48:00

There are three doors. The probability of a car behind a door is 1/3. You choose one (say door 1). The hoster open a door (call it door 2) without a car behind it, I will then pick door 3. The reason is that, when you choose door 1, you have 1/3 chance to win a car; if you choose door 2 and door 3 you have 2/3 chance to win that car. It means that after the host open door 2, then there is 2/3 chance that there is a car behind door 3.

新用户 · 发表于 2005-3-12 07:24:49

Yes, that is my point, to make sure that she opens does not have a car.

y · 发表于 2005-3-13 06:15:30

I tend to agree with you. However, it seems one can also argue that after the host opens the door 2, it is equivalent as the guest has chosen door 1 and 2.

yma16 · 发表于 2005-3-13 06:21:26

Knowing 2 empty doors is the same as knowing a door with the car

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