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Consider an experiment that consists of rolling two standard six-sided dice (sides are of course numbered(1;2 : : : ; 6). We consider the outcome of the experiment to be the sum of the numbers on top of each dice. One then keeps repeating this experiment. Two players, say player A and player B, decide to bet on these repetitions. Player A bets that outcome 12 will come sooner than two consecutive outcomes 7.
Player B bets exactly opposite, i.e. that two consecutive outcomes 7 will come sooner than outcome 12.
The repetitions continue until one of the players wins.
(a) Can this game be modeled using a Markov Chain? If yes, give the interpretation of the Markov assumption and determine the time steps and the one-step transition matrix.
(b) How likely is that sequence of outcomes f5; 6; 7; 3; 12g will be rolled?
(c) How many times on average an outcome 7 will be rolled before the game stops?
(d) Determine the probability that Player A wins