This question was asked to a friend of mine as a part of interview process for DE Shaw & Co. I liked the question. Pretty basic probability question to test ones thinking process.

My two cents:

If the two players have equal probability of winning, the chance that the game will finish in 2 sets or 3 sets is same.

If one of the players is better then other, the chances of game finishing in 2 sets is more then chances of game finishing in 3 sets.

Say, p is probability of Player A winning a set ; q is the probability of Player B winning a set

and lets assume p > q

If game ends in 2 sets => Player A wins first two games or player B wins first two games; P1 = p*p + q*q

If game ends in 3 sets => Player A and B win first or the second game; P2 = p*q + q*p

And we know that, p^2 + q^2 >= 2 p*q [with minima when p=q]