Dependent probability problem.?
Captain Jessica has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Ishaan and his merciless band of thieves.
If her ship hasn't already been hit, Captain Jessica has probability 2/5 of hitting the pirate ship. If her ship has been hit, Captain Jessica will always miss. If his ship hasn't already been hit, dread pirate Ishaan has probability 3/8 of hitting the Captain's ship. If his ship has been hit, dread pirate Ishaan will always miss. If the Captain and the pirate each shoot once, and the Captain shoots first, what is the probability that the Captain misses the pirate ship, but the pirate hits?
Here is my solution
Captain probability: miss 3/5, hit 2/5
pirate probability: miss 5/8,hit 3/8
P(Capt miss but pirate hits) = (3/5)(3/8) = 9/40 Answer
Is my answer correct?