求助一道概率题，谢谢

tinazyg

Tanya prepared 4 different letters to be sent to 4 different addresses.  For each letter, she prepared an envelope with its correct address.  If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
答案：1/3
这题应该怎么做呢？

zgy32041

这么算 C(1,4) * 1/4 * 2/3 * 1/2 = 1/3

4个当中选一个用C(1,4) = 4

选中的一个有1/4的可能性with its correct address

剩下的3个都wrong address的几率为 2/3 * 1/2（因为最后一个没得选，必然选错，所以只把剩下三个中两个都选错的几率相乘就行）

gongchenglu

Probability that first letter in the right envelope= 1/4
Probability that second letter in wrong envelope = 2/3
Probability that third letter in wrong envelope = 1/2
Probability that forth letter in wrong envelope = 1
然后相乘等于1/3
兄弟。类似的问题你以后直接把题目百度或者google

zgy32041

Probability that first letter in the right envelope= 1/4
Probability that second letter in wrong envelope = 2/3
Probability that third letter in wrong envelope = 1/2
Probability that forth letter in wrong envelope = 1
然后相乘等于1/3
兄弟。类似的问题你以后直接把题目百度或者google

-- by 会员 gongchenglu (2010/10/27 17:48:06)

楼上的需要再乘以一个C(1,4)才能求出1/3。。。。

tinazyg

谢谢~