1. 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 Explain why this probability is equal to the probability that the set of withdrawn balls always contains more white than black balls.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.)

2. A coin that comes up heads with probability p is ?ipped n consecutive times. What is the probability that starting with the ?rst ?ip there are always more heads than tails that have appeared?