Solve in R. Take a game where 2 players take turns. Each player, when it is their turn, has a 20% chance of winning the game. There are 4 states: (1) It is player 1's turn; (2) it is player 2's turn; (3) player 1 has won the game; and (4) player 2 has won the game. We can consider this with a transition matrix. a. What is the 4x4 transition matrix for this game? b. What is the state after 5 turns? What is the probability that the game has ended by that point? c. Consider a case where player 1 goes first. Run the action of the transition matrix many times to determine the probability that player 1 wins the game. d. Consider the case where players flip a coin to go first. What is the initial state, in terms of probabilities of being in each state? Confirm that each player has a 50% chance of winning. e. Suppose in a modified game that player 1 is a bit better than player 2, so that player 1 has a 25% chance winning of their turn (player 2 still has a 20% chance). What is the transition matrix? Consider the initial state from (d). What is the probability of player 1 winning