12. Two red dice and a blue die are rolled. What is the probability that the sum of the scores on the red dice is equal to the score on the blue die?
(A) $1 / 12$
(B) $2 / 27$
(C) $1 / 15$
(D) $1 / 18$
(E) $5 / 72$
Problem 12. The answer is (E).

The sum of the scores of the red dice can equal the score of the blue die only when it is $2,3,4,5,6$. These sums are achieved with probabilities $1 / 36, 2 / 36, 3 / 36, 4 / 36, 5 / 36$ respectively. The probability that the score of the blue die is equal is $1 / 6$ in each case. The overall probability is therefore $1 / 6 \cdot(1 / 36 + 2 / 36 + 3 / 36 + 4 / 36 + 5 / 36) = 15 / 216 = 5 / 72$. (Problem proposed by P. Negrini)