Military radar and missile detection systems are designed to warn a country of a
ID: 3125902 • Letter: M
Question
Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Use the binomial probability distribution function to answer the following questions.
What is the probability that a single detection system will detect an attack?
If two detection systems are installed in the same area and operate independently, what is the sample space of this experiment?
What is the probability that none of the systems detect the attack?
What is the probability that at least one detects the attack?
Would you recommend that multiple detection systems be used? Explain.
Explanation / Answer
1a)
Let X be the number of stations that detect a missile. X has the binomial distribution with n trials and success probability p = 0.90
In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.
1b) n = 2, p = 0.90
P(X 1) = P(X = 1) + P(X = 2)
= 0.18 + 0.81
= 0.99
1c)P(x=0)=1-0.90=0.001
1d)n =3
P(X 1) = P(X = 1) + P(X = 2) + P(X = 3)
= 1 - P(X = 0)
= 1 - 0.001
= 0.999
1e) yes; p(at least 1) becomes very close to 1with multiple systems and the inability to detect an attack would be catastrophic.