Question: Suppose every time a tennis player registers to play a tournament, she enters the qualifying stage. If she wins, then next week she plays in the round of sixteen. Further wins will lead her to weekly matches in the quarter-final, semi-final and final rounds, respectively. If she loses, regardless of the stage, she is out of that tournament, but can start a new one with the exact same structure in the following week. If she wins the final, she starts a new tournament the following week, starting in the quarter-final stage. The probability of winning a match in qualifying, round of 16, quarter- final, semi-final or final rounds is 0.8, 0.6, 0.4, 0.2 and 0.1, respectively. Build a Markov chain that represents the round a player is in on any given week. Describe states and classify them.