Captain Ashley has a ship, the H. M.S Crimson Lynx. The ship is two furlongs from the dread pirate Umaima and her merciless band of thieves. If her ship hasn't already been hit, Captain Ashley has probability 1/2. If her ship has been hit, Captain Ashley will always miss.

If her ship hasn't already been hit, dread pirate Umaima has probability 1/3. If her ship has been hit, dread pirate Umaima will always miss.

If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that both the pirate and the Captain hit each other's ships?