P(win 2 out of 2 games) = P(win first game and win second game) = P(win first game)^2. So want to find the probability of winning a game.To win, either we need A odd and B even or we need A even and B odd.P(A odd) = 3/4P(A even) = 1/4P(B odd) = 2/5P(B even) = 3/5.So P(win first game) = 3/43/5 + 1/42/5 =11/20So final answer is 11^2/20^2 = 121/400/