Re: [理工] [機率]請問一題
※ 引述《z3992270 (Eazon)》之銘言：
: 請問各位高手這題
: 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
{coin0 coin1 coin2 ... coink-1 coink }
prob 0/k 1/k 2/k k-1/k k/k
(head)
first,we need all results in heads,so we can't choose coin0
then P(n次head)=1/k (total k's coins,except coin )
second ,we have to choose (n+1)st head is head
Prob=1/k+2/k+...k/k
so the answer is (*)
: 我自己是把n+1次正面的機率除於n次正面的機率
: 就等於
: k k
: Σ(i/k)^(n+1)/Σ(j/k)^n
: i=0 j=0
: 不知道這樣對不對??
: 請各位大大指點一下 謝謝
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