In a serve and rally competition involving players A and B, each rally that begins with a serve by player A is won by player A with probability pa and is won by player B with probability qa = 1 − pa, whereas each rally that begins with a serve by player B is won by player A with probability pb and is won by player B with probability qb = 1 − pb. The winner of the rally earns a point and becomes the server of the next rally.

(a) In the long run, what proportion of points are won by A?

(b) What proportion of points are won by A if the protocol is that the players alternate service? That is, if the service protocol is that A serves for the first point, then B for the second, then A for the third point, and so on.

(c) Give the condition under which A wins a higher percentage of points under the winner serves protocol than under the alternating service protocol.