War-Game strategist make a living by solving problems of the following type. The

Question

War-Game strategist make a living by solving problems of the following type. There are 6 incoming ballistic missiles(BMs) against which are fired 12 antimissile missiles (AMMs). The AMMs are fired so that two AMM are directed against each BM. The single-shot-kill probability (SKKP) of an AMM is 0.8. The SKKP is simply the probability that an AMM destroys a BM. Assume that the AMMs dont interfere with each other and that an AMM, can, at most destroy only the BM against which it is fired. Compute the probability that:

a) all BMs are destroyed

b) at lease one BM gets throughto destroy the target, and

c) exactly one Bm gets through.

Explanation / Answer

Probability of destorying one BM by to AMMs = 1-P( both do not destroy) = 1-0.2*0.2=0.96

p=0.96,q=0.04, n=6

a) P( all are destoryed)=0.96^6=0.78275

b)P( at least one gets through) = 1-P( none get through) = 1-0.96^6=0.21724

c) P( exactly one)= 6*0.96^5*0.04=0.19568

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