An urn contains n white and m black balls that are removed one at a time. If n > 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 Explain why this probability is equal to the probability that the set of withdrawn balls always contains more white than black balls.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.)