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.
Numerical investigation: Is it generally the case that more frames lead to a reduced chance of a weaker player winning? Devise a spreadsheet which computes the chance of a weaker player winning a match in which the first player to $1, 2, 3, 4, \dots, 17, 18$ frames wins. The world snooker championship final is taken over the best of $35$ frames. In order to have at least a $10\%$ chance of winning such a final, what probability of winning each frame would you need to have? Plot $\log(n)$ against $P(win)$.