Crimson Lynx

Captain Emily has a ship, the H. M. S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves.
If her ship hasn't already been hit, Captain Emily has a probability of 3/5 of hitting the pirate ship. If her ship has been hit, Captain Emily will always miss her.
If her ship hasn't already been hit, dread pirate Umaima has a probability 1/7 of hitting the Captain's ship. If her ship has been hit, dread pirate Umaima will always miss.
If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that the pirate misses the Captain's ship, but the Captain hits?

Correct answer:

p =  18/35

Step-by-step explanation:

$$\begin{gathered} p_1=\frac{3}{5}=0.6 \\ {p}_2=1-\frac{1}{7}=\frac{1\cdot 7}{7}-\frac{1}{7}=\frac{7}{7}-\frac{1}{7}=\frac{7-1}{7}=\frac{6}{7}\doteq 0.8571 \\ p=p_1\cdot p_2=\frac{3}{5}\cdot \frac{6}{7}=\frac{3\cdot 6}{5\cdot 7}=\frac{18}{35}=0.5143 \end{gathered}$$

Try another example