Captain Ben has a ship, the H. M. S Crimson Lynx. The ship is four furlongs from the dread pirate Umaima and her merciless band of thieves.
If his ship hasn't already been hit, Captain Ben has probability 3/4 of hitting the pirate ship. If his ship has been hit, Captain Ben will always miss.
If her ship hasn't already been hit, dread pirate Umaima has probability 1/2 of hitting the Captain's ship. 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?
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