推 debdeb :謝謝，我先研究一下XD 02/10 08:49
※ 引述《debdeb ()》之銘言：
: Consider k urns Ui, i=1,...,k, each of which contain m white balls and
: n black balls. A ball is drawn at random from urn U1 and is placed in urn
: U2. Then a ball is drawn at random frm urn U2 and is placed in urn U3 etc.
: Finally, a ball is chosen at random from urn Uk-1 and is placed in urn Uk.
: A ball is then drawn at random from urn Uk. Compute the probability that
: this last ball is black.
: 請問這題該怎麼下手？
: 我先試解k=3，但完全歸納不出個頭緒來
: 麻煩指點一下，謝謝！
假設P(k)=在第k個甕取出黑球的機率
則P(1)=n/(m+n)
P(k)=P(k-1)*(n+1)/(m+n+1) + [1-P(k-1)]*(n)/(m+n+1)
=(n+P(k-1))/(m+n+1)
可得P(2)=[n+P(1)]/(m+n+1) = (mn+n^2+n)/(m+n)(m+n+1) = n/(m+n)
可知P(k)= n/(m+n) for k≧1
(應該沒解讀錯吧??)
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