12. Laura paints the entire surface of a wooden cube blue, then cuts it into $6^{3}=216$ equal smaller cubes. By mixing the smaller cubes and randomly picking one, what is the probability that Laura finds one with exactly one blue face?
(A) $9 / 24$
(B) $32 / 81$
(C) $1 / 2$
(D) $1 / 3$
(E) $4 / 9$
Problem 12. The correct answer is (E).

For each of the cube's faces, there are $4^{2}=16$ small cubes that have one face painted blue. Therefore, in total, there are $6 \cdot 16$ small cubes with one blue face. The probability of drawing one of these is thus $\frac{6 \cdot 16}{6^{3}}=\frac{4}{9}$.