Captain Daniel has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Stephanie and her merciless band of thieves. If his ship hasn't already been hit, Captain Daniel has probability 3/4 of hitting the pirate ship. If his ship has been hit, Captain Daniel will always miss. If her ship hasn't already been hit, dread pirate Stephanie has probability 1/7 of hitting the Captain's ship. If her ship has been hit, dread pirate Stephanie 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?

There is no way for them to hit each other's ships if the pirate shoots first and they each shoot once. In the description of the question, it says that if the Captain's ship is hit, then he will always miss his next shot. So if they each shoot once, and the Pirate hits the captain's ship, the Captain will always miss, so there is no way he will hit the Pirate's ship in return.