Detecting Missile Attacks. 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 0.90 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions:

Qs. 1 What is the probability that a single detection system will detect an attack?

Qs. 2 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? Hint: "at least one" implies all possible cases when one system and both systems can detect the attack. P(at least 1)=f(1)+f(2) where x=1,2 is the number of successes.

Qs. 3 If three 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? Hint: "at least one" implies all possible cases when one system, two systems and all three systems can detect the attack. P(at least 1)=f(1)+f(2)+f(3) where x=1,2,3 is the number of successes.

Qs. 4 Would you recommend that multiple detection systems be used? Explain.

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