※ 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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