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 \dfrac{1}{2} 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. If her ship has been hit, Captain Ashley will always miss. If her ship hasn't already been hit, dread pirate Umaima has probability \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, 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?
Answers
Given : If his ship hasn't already been hit, Captain Ben has probability 2/3, of hitting the pirate ship.
If his ship has been hit, Captain Ben will always miss.
If his ship hasn't already been hit, dread pirate Luis has probability, 1/ 3, of hitting the Captain's ship.
If his ship has been hit, dread pirate Luis will always miss.
Captain and the pirate each shoot once, and the pirate shoots first,
To Find : what is the probability that both the pirate and the Captain hit each other's ships
Solution:
probability that both the pirate and the Captain hit each other's ships
pirate shoots first,
probability that pirate hits the Captain's ship = ( 1/3)
If Captain ship has been hit, Captain Ben will always miss probability that captain hit = 0
Hence probability = (1/3)0 = 0
probability that both the pirate and the Captain hit each other's ships = 0
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