作者erichuyuju (erichyu)
看板GRE
標題[計量] 挑戰GRE計量170之二<解答>
時間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
此題主要考條件機率，關鍵句在 The combind weight of the first pair is equal to
the combined weight of the second pair.
兩組取得的錢幣重量在一樣的條件下，兩組(4個錢幣)都是真幣的
機率為多少?
兩組前後取得4個錢幣重量均相同情形有兩種:
(1)兩組前後4個均為真幣機率:8C4/10C4=(8/10)*(7/9)*(6/8)*(5/7)=1/3
(2)第一組中一真一偽，第二組中也是一真一偽；
其機率:[(8C1*2C1)/10C2]*[(7C1*1C1)/8C2]=(8/10)*(2/9)*(1/8)*(7/7)*4=4/45
題目所求:兩組重量相同情況下，四個錢幣均為真幣的機率=(1/3)/(4/45+1/3)=15/19---
即為答案。
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1F：推 jimmyace : 發現我題意離解錯誤 06/03 07:23
2F：→ jimmyace : 已哭 06/03 07:24
3F：→ kira1116 : 我是覺得算的時候直接拿（兩組一真ㄧ偽）除以（兩 06/03 08:05
4F：→ kira1116 : 組一真一偽+兩組兩真）就好了 基本上兩個的分母都是 06/03 08:05
5F：→ kira1116 : 一樣（即10個先任取2個再乘上剩下8個任取2個） 如 06/03 08:05
6F：→ kira1116 : 此可省下計算時間 06/03 08:05