AMC 12 2010b Problem 18

A frog makes $3$ jumps, each exactly $1$ meter long. The directions of the jumps are chosen independently at random. What is the probability that the frog's final position is no more than $1$ meter from its starting position?

\textbf{(A)}\ \dfrac{1}{6} \textbf{(B)}\ \dfrac{1}{5} \textbf{(C)}\ \dfrac{1}{4} \textbf{(D)}\ \dfrac{1}{3} \textbf{(E)}\ \dfrac{1}{2}