A single game of snooker is called a frame. In the first round of a snooker tournament, the matches are played over eleven frames (so the first player to win six frames wins the match). In the later rounds matches are played over 15 frames. Assume that each player has steady nerves and his chance of winning any frame (irrespective of who starts) is constant.
In the problem Snooker you were asked to find the probability that a player wins a match over fifteen frames, given that his chance of winning any frame is $0.4$. You should now find the probability that this player wins a match over eleven frames.
It is believed that the weaker players have a better chance of winning the matches over eleven frames than they do over fifteen frames. Do your results confirm this or not?
Does this surprise you, or not? Why?