Question: (i) Modify Example 4.20 by assuming that in each game, the player may win with probability p, lose with probability q, or draw (so that

(i) Modify Example 4.20 by assuming that in each game, the player may win with probability p, lose with probability q, or draw (so that his fortune does not change)

with probability r, where p + q + r = 1. Find the transition probability matrix in this case. (ii) Modify Example 4.21 same way as in (i). Write the analogue to the equation

(4.26) for the probability of ruin and solve it.

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