Suppose that independent missiles A, B, C have probabilities .4, .5, and .6 of h

Question

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.

Explanation / Answer

a) 1- 0.6*0.5*0.4 = 0.88 b) 0.4*0.5*0.4 + 0.6*0.5*0.4+0.6*0.5*0.6 =0.38 c) 0.4*0.5*0.4=0.08

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