AMC 12B 2010 Problem 18

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

Answer Choices
A. \dfrac{1}{6}
B. \dfrac{1}{5}
C. \dfrac{1}{4}
D. \dfrac{1}{3}
E. \dfrac{1}{2}