(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

(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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 0.70 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 be used because P(at least 1) for multiple systems very close to 1.

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