We can see that this is dependent probability. We can find dependent probability of happening event A then event B by multiplying probability of event A by probability of event B given that event A already happened.
In our case event A is pirate hitting captain's ship and event B is captain missing pirate's ship.
We have been given that pirate shoots first so pirate's ship can't be hit before pirate shoots his cannons. So probability of hitting captain's ship is 1/3.
We have been given that if Captain Ben's ship is already hit then Captain Ben will always miss. So the probability of Captain missing the dread pirate's ship given the pirate Luis hitting the Captain ship is 1.
Now to find probability that pirate hits Captain, but Captain misses we will multiply our both probabilities.
[tex]\text{Probability pirate hits captain but captain misses}=\frac{1}{3} \cdot1=\frac{1}{3}[/tex]
Therefore, our probability that pirate hits Captain but Captain misses will be [tex]\frac{1}{3}[/tex].
