(b) Alice and Bob are playing a game of chance consisting of repeated rounds in which each has an equal chance of winning. The winner will be the first to win ten rounds. After 16 rounds Alice has won 9 and Bob has won 7. (i) Explain why the game will be decided in at most three more rounds. (ii) Draw a tree diagram showing the possible outcomes of the next three rounds of the game. (iii) Find the respective probabilities that Alice and Bob win the game.

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