3/13 Military radar and missle detection systems are designed to warn a country

Question

3/13

Military radar and missle detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection systen ti identify an attack and issue the warning. Assume that a paqrticular detection system has a .90 probability of detecting a missle attack. Answer the following questions using the binomial probability distribution:

a. What is the probablity that one system will detect an attack?

b. If two detections 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 systems be operated? Why?

Explanation / Answer

Given particular detection system has a .90 probability of detecting a missle attack

a) Probability that a single detection system will detect an attack = 0.90

b) If two detections are installed in the same area and operate independently what is the Probability that at least one of the systems will detect the attack

P(atleast one) = 1- p(detect none)

= 1- 0.1^2

= 1- 0.01

= 0.99

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

P(atleast one) = 1- p(detect none)

= 1- 0.1^3

= 1-0.001

= 0.99

d) Yes, the probabilty for multiple systems becomes very close to 1. The higher the probabilty the radar detection will be high. The probability for multiple systems is higher then probability for system. So I recommend multiple systems to be operated

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