Re: [推理] 富翁的遺產
看板puzzle (益智遊戲 - 數獨,拼圖,推理,西洋棋)作者utomaya (烏托馬雅)時間14年前 (2010/11/02 10:41)推噓5(5推 0噓 76→)留言81則, 6人參與討論串15/19 (看更多)
其實只要簡單幾句話 ,就可以解釋這個現象了
富翁的2份財產,只有兩種值
不管哥哥拿到哪一份,假設他拿到的是L
另一份不管是2L還是L/2,只可能存在一種,
L跟L/2跟2L是不可能同時存在的。因為富翁的2份財產只有兩種值
所以哥哥應該清楚知道L跟L/2,或L跟2L,這兩種只可能存在一種
按照維基的期望值解釋
http://zh.wikipedia.org/zh-tw/%E6%9C%9F%E6%9C%9B%E5%80%BC
一個離散性隨機變數的期望值(或數學期望、或均值,亦簡稱期望)是試驗中每次可能結
果的機率乘以其結果的總和。
哥哥雖然不知道弟弟的錢是2L還是L/2,但他知道這兩種值只可能存在一種
另一個不可能存在的值,既然不可能存在,其機率當然是零
弟弟的錢是真實存在的,其機率為1(總機率必須為1)
假設弟弟的錢是S
哥哥交換後的期望值 = 2L或L/2不可能存在的那一個*0 + S*1 = S
所以哥哥交換後的期望值就是弟弟的錢,
反之弟弟也一樣,交換後的期望值就是哥哥的錢,
很直觀的結論,也符合現實
至於乘0的那一個是L還是L/2? 無所謂,反正乘起來都是0,
只要富翁的財產不是無限大就好
這時候發現0還真是好用!!!
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※ 編輯: utomaya 來自: 219.70.181.249 (11/02 10:52)
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