※ 引述《debdeb ()》之铭言： : 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. : 请问这题该怎麽下手？ : 　 我先试解k=3，但完全归纳不出个头绪来 : 　 麻烦指点一下，谢谢！ 假设P(k)=在第k个瓮取出黑球的机率 则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 (应该没解读错吧??) --

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