Mr. VG is a coach of a good soccer team, but the owner is very unforgiving. If he loses three games in a row in the coming season, he will be automatically fired. So, whenever he loses two games in a row, he bribes the referees in the next game, ensuring that his team wins it. Otherwise, his team wins any game independently with probability 0.8. The season is about to begin. (a) Determine the transition probability matrix of the Markov chain whose state is the number of consecutive games he has lost before the coming game. (b) Determine the probability that his team wins game 3 and loses game 6. (c) Compute the proportion of games (in a long season) his team wins. d) Compute the proportion of games his team wins honestly.