作者erichuyuju (erichyu)
看板GRE
标题[计量] 挑战GRE计量170之二<解答>
时间Wed Jun 3 03:20:07 2015
Two counterfeit coins of equal weight are mixed with 8 identical
genuine coins. The weight of each of the counterfeit coins is
different from the weight of each of the genuine coins. A pair of coins
is selecd at random without replacement from the 10 coins. A second pair
is selected at random without replacement from the remaining 8 coins.
The combind weight of the first pair is equal to the combined weight
of the second pair. What is the probability that all 4 selected coins
are genuin?
(A) 7/11 (B) 9/13 (C) 11/15 (D) 15/19 (E) 15/16
此题主要考条件机率，关键句在 The combind weight of the first pair is equal to
the combined weight of the second pair.
两组取得的钱币重量在一样的条件下，两组(4个钱币)都是真币的
机率为多少?
两组前後取得4个钱币重量均相同情形有两种:
(1)两组前後4个均为真币机率:8C4/10C4=(8/10)*(7/9)*(6/8)*(5/7)=1/3
(2)第一组中一真一伪，第二组中也是一真一伪；
其机率:[(8C1*2C1)/10C2]*[(7C1*1C1)/8C2]=(8/10)*(2/9)*(1/8)*(7/7)*4=4/45
题目所求:两组重量相同情况下，四个钱币均为真币的机率=(1/3)/(4/45+1/3)=15/19---
即为答案。
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1F：推 jimmyace : 发现我题意离解错误 06/03 07:23
2F：→ jimmyace : 已哭 06/03 07:24
3F：→ kira1116 : 我是觉得算的时候直接拿（两组一真ㄧ伪）除以（两 06/03 08:05
4F：→ kira1116 : 组一真一伪+两组两真）就好了 基本上两个的分母都是 06/03 08:05
5F：→ kira1116 : 一样（即10个先任取2个再乘上剩下8个任取2个） 如 06/03 08:05
6F：→ kira1116 : 此可省下计算时间 06/03 08:05