A team play a series of games with win, lose, or draw outcomes. The transition probabilities between winning, losing, and drawing are averaged over a long time and treated as independent: Loss Draw Win Loss 0.3 0.4 0.3 Draw 0.4 0.5 0.1 Win 0.2 0.4 0.4 A. If the team wins two games in a row, what is the probability that it will draw its next game? B. On average the team wins 50% of the time, draws 20% of the time, and loses 30% of the time. Given this, what is probability that it will win 3 games from now? C. If the team is coming off a losing streak of 3 games, what is the chance that it will not lose its next 2 games? D. The team travels on two different buses, and the travel times are exponentially-distributed with means µ1 and µ2 hours, respectively. Derive the probability of the first bus arriving first.
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