14 7 Snooker is a sport played between two players. The players participate in a number of games, called Frames, each of which is won by one of the players. In the final match of the Snooker World Championship, the winner is the first player to win 18 Frames. The Frames are played in four sessions, as follows: Session 1 (Sunday afternoon) 8 Frames Session 2 (Sunday evening) 9 Frames Session 3 (Monday afternoon) (up to) 8 Frames Session 4 (Monday evening) (up to) 10 Frames [Note that the maximum possible number of Frames is 35, with a score of 18–17] You may assume that the probability of a player winning each Frame remains constant, with results between Frames being independent of one another. This year’s final is to be played between Gordon and Ping. Gordon is considered to be a better player than Ping, with the probability of Gordon winning a Frame equal to 0.55 (a) After the first two sessions (17 Frames), find the expected number of Frames won by Gordon. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (b) After the first two sessions, find the probability that Gordon will have won more Frames than Ping. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________