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142780 2008 年 11 月 25 日 15:30 Reading (loading. ..) Comments (1) Category: Personal Diary
This question the first time, probably written in 1889 约瑟夫贝特朗 the book Calcul des probabilités.
In this book,
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with clear limits,
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participants selected one of three doors. He did not know what is inside.
behind each door hosts know what.
host must open one of the remaining doors,
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host a goat will always pick a door.
If the competitor has to pick a goat door, the host must pick a goat door to another fan.
If the player has to pick a car door ,
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Participants will be asked whether to keep his original choice or switch to choose which door the rest.
conversion option to increase participants a chance ?
answer is:
when the participants turned to another door instead of continuing to maintain the original choice, the opportunity to win the car will be doubled.
There are three possible scenarios, all have equal probability (1 / 3)
One participant picked the goat,
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new new balance shoes, the host picked goats II. Conversion will win the car. Participants pick the goat
II, the hosts pick No. goats. Conversion will win the car.
contestants pick car, the host of any one pick two goats. Conversion will fail.
in the first two cases,
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third situation is the only contestant to win by keeping the situation in the original selection.
because the three cases, there are two choices to win by conversion, so the choice by converting the probability of winning is 2 / 3.
another explanation:
Suppose you select will always be converted, then the only possibility is to win an election without a car door,
because the moderator will open another one then there will goat door, eliminating the conversion after the election to choose the possibility of another sheep.
for a total of three doors, with the total number of goats is a two door,
so the conversion option and the probability of winning the car is 2 / 3, and select the first choice probability of a goat, like the door.
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