question archive You invented a new card game that is played with 9 cards
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 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.
a) Define states and state space.
b) Construct one-step transition probability matrix.
c) Find all classes and determine transience/recurrence of each class.
d) Starting the game with 9 cards (initial conditions), determine the mean time spent in the game until it is over.
