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Assume 4 teams, labelled T1, T2, T3, T4, compete in a tournament. Assume that the probability...

Assume 4 teams, labelled T1, T2, T3, T4, compete in a tournament. Assume that the probability of winning a game is random. Team T1 beats any team it plays with probability p > 1/2. Teams T2, T3, and T4 have the same probability q = 1/2 of beating each other and probability (1 − p) of being team T1. If team T1 plays T2 and team T3 plays T4, and the winner of each game play in the finals, what is the probability that (assuming all the games are independent): (a) team T1 wins? (b) team T2 wins? (c) team T3 wins? (d) team T4 wins?

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