Two cannons each shoot one shell at the target. The probabilty that the first cannon hits the target is 0.2, and the probability that the second cannon hits the target is 0.6. The target will be destroyed if both cannons hit the target, but if just one cannon hits the target, the probability of target being destroyed is 0.3. What is the probability that the target is destroyed after two shots?

I think, I have to use the Bayes theorem here.

First event is C1, first cannon hits the target.

Second event is C2, second cannon hits the target.

Third event is T, target is destroyed.

$\displaystyle P(C1) = 0.2$

$\displaystyle P(C2) = 0.6$

This is conditional probability:

$\displaystyle P(T | C1 * C2) = 1$

$\displaystyle P(T | C1 + C2) = 0.3$

is this OK?, because the text is a little complex here.