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 0.80 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions.

(a) What is the probability that a single detection system will detect an attack?

(b) If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

(c) If three systems are installed, what is the probability that at least one of the systems will detect the attack?

(d) Would you recommend that multiple detection systems be used? Explain.

Multiple detection systems (should or should not) be used because P(at least 1) for multiple systems (is or is not) very close to 1.

Answer 1

Answer:

a)

Here the probability that a single detection system will detect an attack = 0.80

b)

probability that a single detection system will not detect an attack = 1 - probability that a single detection system will detect an attack

= 1 - 0.80

= 0.20

probability that at least one of the systems will detect the attack = 1 - P(both will not detect)

= 1 - 0.20^2

= 0.96

c)

probability that at least one of the systems will detect the attack 1 - P(all three)

= 1 - 0.20^3

= 0.992

d)

Here would recommended to use multiple detection systems as the probability of detection increases when multiple detection systems are used.