Standing on the origin of an \(xy\)-coordinate plane, John takes a 1-unit step at random in one of the following

[M7MBA]

Standing on the origin of an \(xy\)-coordinate plane, John takes a 1-unit step at random in one of the following 4 directions: up, down, left, or right. If he takes 3 more steps under the same random conditions, what is the probability that he winds up at the origin again?

(A) \(\dfrac7{64}\)
(B) \(\dfrac9{64}\)
(C) \(\dfrac{11}{64}\)
(D) \(\dfrac{13}{64}\)
(E) \(\dfrac{15}{64}\)

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT