(a) Tenuka and Olivia enjoy playing a particular game for two players. The game always results in one winner and one loser so that the game can never end in a draw. When they play the game, the probability that Tenuka wins is 0.6. They decide to play a tournament in which they will play the game multiple times. The tournament will continue until one of the players has won five games more than the other player. (i) Explain why this tournament could be considered as a Gambler's ruin problem played between Tenuka and Olivia each starting with 5 with the loser passing the winner 1 in each round. (ii) Hence calculate the probability that in any tournament, Olivia is declared the winner. (iii) Find the average number of games played in any tournament. 12 [2