Markov chains

2) Markov Chains 8:. Probability 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: --- A If the team wins two games in a row, what is the probability that it will draw its next game? ; 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? Q 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? ; The team travels on two different buses, and the travel times are exponentially-distributed with means #1 and #2 hours, respectively. Derive the probability of the rst bus arriving rst