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Captain Ishaan has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Luis and his merciless band of thieves. The Captain has probability \dfrac{4}{5} 5 4 ​ start fraction, 4, divided by, 5, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{7} 7 1 ​ start fraction, 1, divided by, 7, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?

Respuesta :

Answer: [tex]\frac{4}{35}[/tex]

Step-by-step explanation: The probability of Captain Ishaan hitting the pirate's ship is:

P(A) = [tex]\frac{4}{5}[/tex]

The probability of the pirate hitting Captain's ship is:

P(B) = [tex]\frac{1}{7}[/tex]

So, the probability of both hitting each other is a probability of A and B occuring, which means:

P(A) . P(B) = [tex]\frac{4}{5} . \frac{1}{7}[/tex]

P(A) . P(B) = [tex]\frac{4}{35}[/tex]

The probability of both the pirate and the Captain hit each other's ship is

[tex]\frac{4}{35}[/tex] or 11.43%

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