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 \dfrac{3}{4}
4
3
start fraction, 3, divided by, 4, end fraction 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 \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction 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?
We are told that if the Captain's ship has been hit, he will always miss and since the pirate is shooting first, the captain's ship could be hit. So the probability that both of them hit each other's ship is 0 because if the pirate hits the Captain's ship, he will always miss. 1/2 * 0 = 0
There is no way for both of them to hit each other's ships because if their ships have been hit, they will always miss.
