Suppose that independent missiles A, B, C have probabilities .4, .5, and .6 of hitting the enemy's headquarters, respectively. Assume that the enemy's headquarters will be destroyed with a probability .3, if hit by a single missile, .6 if hit by two missiles, and 1 if hit by all three missiles.
(a) Find the probability that the headquarters is destroyed.
(b) Find the probability that the headquarters is destroyed by a single missile knowing that it is destroyed.
(c) Find the probability that the headquarters is destroyed by missile A knowing that it is destroyed.