※ 引述《msu (do my best)》之銘言： : 請問這題 : There are k+1 coins in a box. : The ith coin will,when flipped,turn up head withprobability i/k : ,i=0,1,...,k . A coin is randomly slected from the box and is then : repeatedly filpped. : If the first n flips all results in heads, what is the conditional : probability that the (n+1)st flip will do likewise? : 答案寫 : P((n+1)st head | n次head) : 1 1 2 k-1 k k+1 : =--(--+--+.....+---+--)=---- : k k k k k 2k : ^^ : 可是不懂第一項 1/k怎麼來的@@ : 請問誰會呢? Let A denote "the ith coin is selected" event P(A)=i/(k+1) Let B denote "the jth coin flipped the first n times are all head" event P(B)=(j/k)^n Let C denote "the jth coin flipped the (n+1)th flip is head" event P(C)=j/k Let D denote "the answer" event P(D) = P(C|A∩B) = P(A∩B∩C)/P(A∩B) = Σ(i/k)^(n+1)/Σ(j/k)^n -- 大部份人都是「別人」。他們的想法是別人的意見 他們的生活模仿別人，甚至他們的熱情也只是承襲引用別人的…… 只有去除掉一切的文化，才能找到自己。 Oscar Wilde - 王爾德 --

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