Question

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 \dfrac{2}{5} 5 2 ​ start fraction, 2, divided by, 5, end fraction 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 \dfrac{3}{8} 8 3 ​ start fraction, 3, divided by, 8, end fraction 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?

Answer 1

Answer:

9/40

Step-by-step explanation:

Captain Jessica shoots first.  This means her ship has not already been hit, which means she has a 2/5 chance of hitting the pirate ship.  This also means she has a 1-2/5 = 3/5 chance of missing the pirate ship.

Since Captain Jessica misses, dread pirate Ishaan has a 3/8 chance of hitting the captain's ship.  This means he has a

3/5(3/8) = 9/40 chance of the captain missing the pirate and the pirate hitting the captain.