Captain Ben has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Luis and his merciless band of thieves.
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.
If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that the pirate hits the Captain's ship, but the Captain misses?
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 the pirate hits the Captain's ship, but the Captain misses
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 miss = 1
Hence probability = (1/3)1 = 1/3
probability that the pirate hits the Captain's ship, but the Captain misses = 1/3
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