Answers
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
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