Give the state transition diagram of the process

Reference no: EM131828560

Ben and Jerry play a series of games of cards. During each game each player bets a $1, and whoever wins the game gets the $2. Sometimes a game can end in a tie, in which case neither player loses his money. Ben is a better player than Jerry and has a probability 0.5 of winning each game, a probability 0.3 of losing each game, and probability 0.2 of tying with Jerry. Initially Ben had $9, while Jerry had $6, and the game is over when either player is wiped out.

a. Give the state transition diagram of the process.

b. If r_k denotes the probability that Ben is ruined, given that the process is currently in state k, obtain an expression for r_k in the first game when the process is in state k.

Reference no: EM131828560

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