AMC 12 2015b Problem 9

Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is $\tfrac{1}{2}$, independently of what has happened before. What is the probability that Larry wins the game?

\textbf{(A)} \dfrac{1}{2} \textbf{(B)} \dfrac{3}{5} \textbf{(C)} \dfrac{2}{3} \textbf{(D)} \dfrac{3}{4} \textbf{(E)} \dfrac{4}{5}