Question

Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Michael and his merciless band of thieves.

The Captain has probability \dfrac{1}{2}

2

1

​

start fraction, 1, divided by, 2, 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}{6}

6

1

​

start fraction, 1, divided by, 6, 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?

Answer 1

`(1)/(12)`

Explanation:

Probability of the captain hitting the pirate ship
`=(1)/(2)`

Probability of the pirate hitting the captain's ship
`=(1)/(6)`

If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship

=P(Captain Hits AND Pirate Hits)

=P(Captain Hits) X P(Pirate Hits)

`=(1)/(2) X (1)/(6)\\\\=(1)/(12)`