A and B play a game with the following rules: A starts with $1, and B starts with $2. A fair die is rolled to determine the outcome of each turn: If a 1, 2, or 3 is rolled, B gives A $1. If a 4 is rolled, B gives A all its money. For any other outcome, A gives B $1. The game ends when a player runs out of money, and this player loses the game. Consider the following states in your analysis: X: A has $1 Y: A has $2 W: A has $3 . L: A has $0 (a) Find the transition matrix of the given states. (b) Calculate the probability of A winning the game. (c) Determine the expected length of the game. Tir 1