A missile protection system is set up in a particular zone. The system consists

Question

A missile protection system is set up in a particular zone. The system consists of n radar sets operating independently. Each set has a probability of 0.95 of detecting a missile which enters the zone. Suppose that there are 6 radar sets operating in a particular day (ie, n = 6), and a missile enters the zone. (a) What is the probability that at least 5 sets detect the missile? (b) What is the probability that none of the sets detect the missile? (c) Given that a missile is detected by at least one set, what is the conditional probability that it is only detected by exactly one set?

Explanation / Answer

Ans:

Use binomial distribution:

n=6,p=0.95

P(x=k)=6Ck*0.95k*0.056-k

a)P(x=5,6)=6C5*0.955*0.051+6C6*0.956

=0.2321+0.7351

=0.9672

b)P(x=0)=(1-0.95)^6=0

c)P(x=1/x>=1)=P(x=1)/P(x>=1)

Now,

P(x>=1)=1-P(x=0)=1-0=1

P(x=1)=6C1*0.951*0.055=0.000002

P(x=1/x>=1)=0.000002

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