Military radar and missile detection systems are designed to warn a country of a
ID: 3060416 • 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 .87 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?
(to 2 decimals)
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?
(to 4 decimals)
c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?
(to 4 decimals)
d. Would you recommend that multiple detection systems be used?
- Select your answer -YesNo
Explanation / Answer
a.Let X be the number of stations that detect a missile. X has the binomial distribution with n trials and success probability p = 0.87
b.P(at least one) = 1-P(none detect)
= 1 -0.13^2
= 1-0.0169
=0.9831
c. probability that at least one of the systems will detect the attack
= 1 - 0.13^3
= 1 - 0.0021
= 0.9979
d.yes, you get higher prob of detection with multiple systems.