Two players are playing a coin tossing game. Player A wins $1 when the coin comes up heads and loses $1 when it comes up tails. Player B is unaware that the coin is weighted so that p(heads)=.55. They start with $4 divided in one dollar units between them. They play until one player has no money (is "ruined").

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

B)Write G in the form:

IO

RQ

C) Find the Fundamental Matrix, F.

D) On average, how many times will player A have $3 if player A starts with $2?

E) On average, how many plays will it take until one of the players is ruined if player A starts with $3?

G) Find FR.

H) Find the probability that player A will be ruined if each player starts with $2.