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, end fraction 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

Answer:  The probability that the pirate hits the Captain's ship, but the Captain misses is $\frac{1}{3}$ .

Step-by-step explanation:

As per given information in the question, it is clearly evident that the second event is dependent on the outcome of the first event. The probability thus involved in these events is known as dependent probability.

In order to find the dependent probability we multiply the individual probabilities which is based on the outcome of the first event.

To Simplify, Let us consider the event where pirate hits the captain's ship as A and Captain missing the pirate ship as B.

Now, as per the given information in the question, we know that pirate shoots first, which also means that captain has not attacked the pirate's ship because captain hasn't shot yet.

As per given data in the question, probability of hitting captain's ship is $\frac{1}{3}$ .

So, probability of event A = $\frac{1}{3}$ .

In question we are been asked to find the probability of pirate hitting and captain missing.

Let us assume that pirate hits the captain's ship, so that dependent probability can be found.

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.

So, probability of event B = 1 .

Now to find probability that pirate hits Captain, but Captain misses we will multiply our both probabilities, i.e. A X B .

The probability that the pirate hits the Captain's ship, but the Captain misses = $\frac{1}{3} \cdot1=\frac{1}{3}$

Therefore, our probability that pirate Luis hits Captain Ben's ship but Captain Ben misses will be $\frac{1}{3}$ .

Answer 2

Given : 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.

Captain and the pirate each shoot once, and the pirate shoots first,

To Find :  what is the probability that the pirate hits the Captain's ship, but the Captain misses

Solution:

probability that both the pirate and the Captain hit each other's ships

pirate shoots first,

probability that  pirate hits the Captain's ship,   = ( 1/3)

If Captain ship has been hit, Captain Ben will always miss probability that captain miss = 1

Hence probability = (1/3)1   = 1/3

probability that the pirate hits the Captain's ship, but the Captain misses = 1/3

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