2017 AMC 12B Problem 20

Real numbers x and y are chosen independently and uniformly at random from the interval (0,1). What is the probability that \lfloor\log_2x\rfloor=\lfloor\log_2y\rfloor?

\textbf{(A)}\ \frac{1}{8}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.