Ant Amelia starts on the number line at 0 and crawls in the following manner. For n=1,2,3, Amelia chooses a time duration t_{n} and an increment x_{n} independently and uniformly at random from the interval (0,1). During the n th step of the process, Amelia moves x_{n} units in the positive direction, using up t_{n} minutes. If the total elapsed time has exceeded 1 minute during the n th step, she stops at the end of that step; otherwise, she continues with the next step, taking at most 3 steps in all. What is the probability that Amelia’s position when she stops will be greater than 1 ?
Answer Choices
A. \dfrac{1}{3}
B. \dfrac{1}{2}
C. \dfrac{2}{3}
D. \dfrac{3}{4}
E. \dfrac{5}{6}