3.6. Two teams, A and B, are to play a best of seven series of games.

Suppose that the outcomes of successive games are independent, and each is won by A with probability p and won by B with probability 1 - p. Let the state of the system be represented by the pair

(a, b), where a is the number of games won by A, and b is the number of games won by B.

Specify the transition probability matrix. Note that a + b s 7 and that the series ends whenever a = 4 or b = 4.