A noisy A/B binary classification problem has true distribution over input–output (x, y) pairs as follows: (0, A) w.p. (with probability) 1/2, (1, A) w.p. 1/6, and (1, B) w.p. 1/3. On input x = 0, a probabilistic classifier gives output distribution 〈1, 0〉 (i.e., probability 1 on A, and probability 0 on B) and on input x = 1 it gives output distribution 〈1/4, 3/4〉. What is the logarithmic loss (base 2) of this classifier?