Captain William has a ship, the H. M.S Crimson Lynx. The ship is five furlongs from the dread pirate Emily and her merciless band of thieves.

If his ship hasn't already been hit, Captain William has probability 1/3 of hitting the pirate ship. If his ship has been hit, Captain William will always miss.

If her ship hasn't already been hit, dread pirate Emily has probability 1/7 of hitting the Captain's ship. If her ship has been hit, dread pirate Emily will always miss.

If the Captain and the pirate each shoot once, and the Captain shoots first, what is the probability that the Captain hits the pirate ship, but the pirate misses?