A and B play a series of games. Each game is independently won by player A with probability

0.55 and by player B with probability 0.45. They continue playing the games

until the total number of wins of one of the players is two greater than of the other

player. First describe the list of outcomes in the sample space, and then use the infinite series to determine the probability that player A is the winner of the series.

Hint: the outcomes for A winning are:

{AA, ABAA, BAAA, ABBAAA, ABABAA, BABAAA, BAABAA, ...}.