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"Football is a simple game; 22 men chase a ball for 90 minutes and at the end, the Germans win." (Gary Lineker, after losing 1990 World Cup semifinal to Germany by penalties) Germany and England are playing for the final at EURO Cup 2020. The game ended in a draw, and the first round of penalty shoot-out has ended 5-5. According to the rules of football, the penalty shoot-out continues until one side scores and the other does not. Assume that England kicks first and for any penalty kick Germany has a probability 0.8 of scoring, and England has a probability 0.7 of scoring.

1. Model this process as a Markov chain and write down the transition probability matrix.

2. Classify the states and identify classes.

3. Find the probability that Germany will win the game.

d Find the expected number of penalty kicks after 5-5.