Captain Nadia has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Tiffany and her merciless band of thieves.
If her ship hasn't already been hit, Captain Nadia 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 Nadia will always miss.
If her ship hasn't already been hit, dread pirate Tiffany has probability \dfrac{2}{7}
7
2
start fraction, 2, divided by, 7, end fraction of hitting the Captain's ship. If her ship has been hit, dread pirate Tiffany 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?
Answers
Given :Captain Nadia has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Tiffany and her merciless band of thieves.
Captain shoots first,
To Find : what is the probability that the Captain misses the pirate ship, but the pirate hits
Solution:
If ship has not been hit
Captain Nadia has probability of hitting the pirate ship = 1/2
=> Captain Nadia has probability of not hitting the pirate ship =1 - 1/2 = 1/2
If ship has been hit
Captain Nadia always miss
If ship hasn't already been hit,
dread pirate has probability of hitting the captain ship = 2/7
dread pirate has probability of not hitting the captain ship = 1-2/7 = 5/7
If ship has been hit
dread pirate always miss
Captain misses the pirate ship, but the pirate hits
Captain misses the pirate ship = 1/2
pirate hits = 2/7
Probability that Captain misses the pirate ship, but the pirate hits = (1/2)(2/7) = 1/7
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