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You invented a new card game that is played with 9 cards

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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 s 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 refer to restart the game with 9 cards or he/she can continue playing. The game s over when there is no card left in both white and black card groups. [35 pts] Define states and state space. Construct one-step transition probability matrix.