Real numbers between 0 and 1, inclusive, are chosen in the following manner. A fair coin is flipped. If it lands heads, then it is flipped again and the chosen number is 0 if the second flip is heads, and 1 if the second flip is tails. On the other hand, if the first coin flip is tails, then the number is chosen uniformly at random from the closed interval [0,1]. Two random numbers x y are chosen independently in this manner. What is the probability that |x-y| > \dfrac{1}{2} ?
Answer Choices
A. \dfrac{1}{3}
B. \dfrac{7}{16}
C. \dfrac{1}{2}
D. \dfrac{9}{16}
E. \dfrac{2}{3}