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找到原因了.大家看.其实关键是在于
# 主持人知道每扇門後面有什麼。
# 主持人必須開啓剩下的其中一扇門,並且必須提供換門的機會。所以这些人为的选择改变了机率.相反,如果主持人什么都不知道.而且可以随机选择的话.就不一样了.
Why the probability is not 1/2
The critical fact is that the host does not always have a choice (whether random or not) between the two remaining doors. He always chooses a door that he knows hides a goat after the contestant has made their choice. He always can do this, since he knows the location of the car in advance. If the host chooses completely at random when he has a choice, and if the car is initially likely to be behind any of the three doors, it turns out that the host's choice does not affect the probability that the car is behind the contestant's door. But even if the host has a bias to one door or another when he has a choice, the probability that the car is behind the contestant's door, so it turns out, can never exceed 1/2, again as long as initially all doors are equally likely. It is never unfavourable to switch, while on average it definitely does pay off to switch. The contestant will be asked if he wants to switch, and there was a 1 in 3 chance that his original choice hides a car and a 2 in 3 chance that his original choice hides a goat. By opening another door and revealing a goat the host has removed one of the two other doors, and the 1 in 3 chance of the contestant's initial door hiding a car means there is a 2 in 3 chance that the other closed door will turn out to hide a car.
[ 本帖最后由 gifox 于 2010-11-26 17:17 编辑 ] |
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