Question

Missile target practice problem (discussed in class but restated here with modified numbers): Suppose that independent missiles A, B and C have probabilities 0.52, 0.48 and 0.375 of hitting a practice target, respectively. Assume that the target will be destroyed with probability 0.25 if hit by a single missile, 0.49 if hit with two missiles and 0.88 if hit by all three missiles. Find:

a. The probability that the target is destroyed.

b. The probability that the target is destroyed by a single missile knowing that it is destroyed.

c. The probability that the target is destroyed by missile B knowing that it is destroyed.

Answer 1

a)P(target destroyed)=P(A hit and not B and C and target destroyed)+P(B hit and not A or C and target destroyed)+P(C hit and not A or B and target destroyed)+P(A and B hit and not C and target destroyed)+P(A and C hit and not B and target destroyed)+P(B and C hit and not A and target destroyed)+P(A and B and C ht and target destroyed)

=0.25*(0.52*(1-0.48)*(1-0.375)+(1-0.52)*0.48*(1-0.375)+(1-0.52)*(1-0.48)*0.375)+0.49*(0.52*0.48*(1-0.375)+0.52*(1-0.48)*0.375+(1-0.52)*0.48*0.375)+0.52*0.48*0.375*0.88

=0.35248

b)

P( destroyed by a single missile |destroyed)

=0.25*(0.52*(1-0.48)*(1-0.375)+(1-0.52)*0.48*(1-0.375)+(1-0.52)*(1-0.48)*0.375)/0.35248=0.288385

c)

The probability that the target is destroyed by missile B given destroyed

=0.25*((1-0.52)*0.48*(1-0.375))/0.35248=0.102133