8.2 Mark and Kevin play a series of games of cards. During each game each player bets $1, and whoever wins the game gets $2. Sometimes a game ends in a tie in which case neither player loses his money. Mark is a better player than Kevin and has a probability 0.5 of wining each game, a probability 0.3 of losing each game, and a probability 0.2 of tying with Kevin. Initially Mark had $9 and Kevin had $6, and the game is over when either player is bankrupt.

a. Give the state-transition diagram of the process.

b. If rk denotes the probability that Mark is ruined, given that the game is