Question

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
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
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?

Answer 1

The probability is 1/7.

If the Captain shoots first, there is a 1/2 chance she will miss the pirate.  Since the pirate ship was not hit, there is a 2/7 chance she will hit the Captain.  The total probability is 1/2(2/7) = 2/14 = 1/7.