A red ball and a green ball are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin k is 2^{-k} for k=1,2,3, \ldots What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?

**Answer Choices**

A. \dfrac{1}{4}

B. \dfrac{2}{7}

C. \dfrac{1}{3}

D. \dfrac{3}{8}

E. \dfrac{3}{7}