We are given $b$ white balls and $n$ black balls ($b,n>0$) which are to be distributed among two urns, at least one in each. Let $s$ be the number of balls in the first urn, and $r$ the number of white ones among them. One randomly chooses an urn and randomly picks a ball from it. (a) Compute the probability $p$ that the drawn ball is white. (b) If $s$ is fixed, for which $r$ is $p$ maximal? (c) Find the distribution of balls among the urns which maximizes $p$. (d) Give a generalization for larger numbers of colors and urns.