A standard set of pool balls contains 15 balls numbered from 1 to 15. Pegleg Woodhull, the famous blind poolplayer, is playing a game of 8-ball, in which the 8-ball must be, the last one hit into a pocket. He is allowed to touch the balls to determine their positions before taking a shot, but he does not know their numbers. Every shot Woodhull takes is successful. (a) What is the probability that he hits the 8-ball into a pocket, on his fi rst shot, thus losing the game? (b) What is the probability that the 8-ball is one of the fi rst three balls he hits? (c) What is the probability that Pegleg wins the game, that is, that the 8-ball is the last ball hit into a pocket?
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