There are two urns. One contains five white balls. The other contains four white balls and one black ball. An urn is selected at random and a ball in that urn is selected at random and removed. This procedure is repeated until one of the urns in empty. The probability that the black ball has not been selected is Binomial(10,5)/2^10. The form of the answer suggests a counting solution. What is being counted?
closed as not a real question by Robin Chapman, Steve Huntsman, Harry Gindi, Wadim Zudilin, Greg Kuperberg Jun 26 2010 at 13:48