Question

Captain Ben has a ship, the H.M.S Crimson Lynx. The ship is five furlongs from the dread pirate Luis and his merciless band of thieves.

If his ship hasn't already been hit, Captain Ben has probability 2/3 of hitting the pirate ship. If his ship has been hit, Captain Ben will always miss.

If his ship hasn't already been hit, dread pirate Luis has probability 1/3 of hitting the Captain's ship. If his ship has been hit, dread pirate Luis will always miss.

If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that the pirate hits the Captain's ship, but the Captain misses?

Answer 1

The probability that the pirate hits the Captain's ship but the Captain misses is 1/9.

Step-by-step explanation:

To find the probability that the pirate hits the Captain's ship but the Captain misses, we need to consider two scenarios: the ship hasn't been hit and the ship has been hit. Let's calculate each scenario:

1. If the ship hasn't been hit: The probability that the pirate hits the Captain's ship is 1/3, and the probability that the Captain misses is 1 - 2/3 = 1/3. Therefore, the probability of this scenario is (1/3) * (1/3) = 1/9.
2. If the ship has been hit: In this case, the Captain will always miss. Therefore, the probability of this scenario is 2/3 * 0 = 0.

Since the pirate shoots first, the probability that the pirate hits the Captain's ship but the Captain misses would be the probability of Scenario 1, which is 1/9.

Answer 2

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.

`\text{Probability pirate hits captain but captain misses}=(1)/(3) \cdot1=(1)/(3)`

Therefore, our probability that pirate hits Captain but Captain misses will be
`(1)/(3)`.