Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questions using the binomial probability distribution:
a. What is the probability that 1 detection system will detect an attack?
b. If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the attack?
c. If 3 systems are installed, what is the probability that at least 1 of the systems will detect the attack?
d. Would you recommend that multiple detection systems be operated? Explain.