(Gambler's Ruin) When Cathy and Jill play checkers, each has probability \ of winning. There is never a tie, and the games are independent in the sense that no matter how many games the girls have played, each girl still has probability 1/2 of winning the next game. After each game the loser gives the winner a quarter. If Cathy has $2.00 to play with and Jill has $2.50 and they play until one of them is broke, what is the probability that Cathy gets wiped out?