Question 139
A piece is initially on the central square of a $5 \times 5$ board. A step of the piece consists of moving to a square chosen at random among those that have exactly one vertex in common with the square the piece is on. What is the probability that after 12 steps the piece is on any one of the corners of the board?
(A) $\frac{1}{3}$
(B) $\frac{4}{25}$
(C) $\frac{1}{6}$
(D) $\frac{4}{13}$
(E) $\frac{1}{4}$
(A) $\frac{1}{3}$
(B) $\frac{4}{25}$
(C) $\frac{1}{6}$
(D) $\frac{4}{13}$
(E) $\frac{1}{4}$