[理工] [機率]請問一題
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
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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