A target is being shoot at by 3 cannons, the cannons shoot at the target independently of each other with a chance of hitting the target of 0.4 . If 1 cannon hits the target it has a 0.3 chance of destroying it, if 2 cannons hit the target they have a 0.7 chance of destroying it, and if 3 cannons hit the target they have a 0.9 chance of destroying it. What is the chance to destroy the target?
The answer should be 0.389
Using a simple bayers theory where i just multiplied the chance to hit with the chance to destroy based on how many cannonballs hit the target taking in consideration to multiply the chance to hit based on how many hit, the answer I got was 0.289 which is quite away from the expected result.