2023 AMC 12A Problem 17

Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance m with probability \dfrac{1}{2^m}. What is the probability that Flora will eventually land at 10?

\textbf{(A)} \dfrac{5}{512} \qquad \textbf{(B)} \dfrac{45}{1024} \qquad \textbf{(C)} \dfrac{127}{1024} \qquad \textbf{(D)} \dfrac{511}{1024} \qquad \textbf{(E)} \dfrac{1}{2}

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