AMC 12 2019b Problem 13

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 $k = 1,2,3....$ What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?

$\textbf{(A) } \frac{1}{4} \textbf{(B) } \frac{2}{7} \textbf{(C) } \frac{1}{3} \textbf{(D) } \frac{3}{8} \textbf{(E) } \frac{3}{7}$