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?

It is given that 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.

Case I:

Let say pirate shoots first and hit the ship of Captain Daniel, now captain Daniel will hit but as we know if his ship has been hit, Captain Daniel will always miss. Thus there is zero possibility of Captain hits Stephanie ship.

Case II

Let pirate shoots first and miss the hit, now captain Daniel will hit but as we know if his ship hasn't already been hit, Captain Daniel has probability 3/4 of hitting the pirate ship. In this case pirate will miss the shoots. Thus, there is zero possibility that the pirate and the Captain hit each other's ships.

Hence, the probability is zero.