AMC 12 2017b 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} \textbf{(B)}\ \frac{1}{6} \textbf{(C)}\ \frac{1}{4} \textbf{(D)}\ \frac{1}{3} \textbf{(E)}\ \frac{1}{2}