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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.