Before a knockout tournament with 2^n players I pick two players.
What is the probability that they have to play against each other
at some point in the tournament?
If the score is 8-8 do I have more chance of winning if the winner
is the first to reach 9 points or the first to reach 10 points?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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?