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. $\dfrac{2}{3}$