Two numbers 'a' and 'b' with 0 <= a <= 1 and 0 <= b <= 1 are chosen at random. The number 'c' is defined by c = 2a + 2b. The numbers 'a', 'b', and 'c' are each rounded to the nearest integer to give 'A', 'B', and 'C', respectively (for example, if a = 0.432 and b = 0.5, then A = 0, B = 1, and C = 2). What is the probability that 2A + 2B = C?