Question

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

The Captain has probability 2/3 of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability 1/ 3
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

The events ' captain's cannon hits pirate ship' and 'pirate's cannon hits captain's ship' are independent. Therefore the probability of both events happening together is the product of the probabilities of the events.

`P(both\ hit)=(2)/(3)*(1)/(3)=(2)/(9)`