47. An urn contains white and m black balls which are removed one at a time....

47. An urn contains ç white and m black balls which are removed one at a time. If ç > m, show that the probability that there are always more white than black balls in the urn (until, of course, the urn is empty) equals

(n - m)/(n + m). Explain why this probability is equal to the probability that the set of withdrawn balls always contains more white than black balls.

(This latter probability is (n - m)/(n + m) by the ballot problem.)