Q4. You invented a new card game that is played with 9 cards. The cards are coloured as three white, three black and three red, and shuffled. The game is played by a single person. The player draws a card in each turn. The drawn card is removed from the deck if it is either white or black. If a red card is picked, the card is not removed from the deck and the game continues. If the situation of 1 white and 1 black card occurs in the game, there is 50% chance that the player may prefer to restart the game with 9 cards or he/she can continue playing. The game is over when there is no card left in both white and black card groups. [35 pts] Construct one-step transition probability matrix. a) Define states and state space. b) c) d) Find all classes and determine transience/recurrence of each class. Starting the game with 9 cards (initial conditions), determine the mean time spent in the game until it is over.