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 \dfrac{1}{2}, independently of what has happened before. What is the probability that Larry wins the game?
Answer Choices
A. \dfrac{1}{2}
B. \dfrac{3}{5}
C. \dfrac{2}{3}
D. \dfrac{3}{4}
E. \dfrac{4}{5}