28.

Two players are playing a coin tossing game. Player A wins $1 if the coin comes up heads and loses $1 if it comes up tails. Player B is unaware that the coin is weighted so that p(heads)=.55. They start with $3 in some way divided between them. They play until one player has no money.

A. Write the transition matrix, P, for this game from player A's point of view.

B. Find the Fundamental Matrix, F, and then state the average number of times player A would have $2 if player A starts with $1.

C. State FR and then state the probability that player A will go broke if player A starts with $1.