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  probability of .95 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 -

yes or no

Answer 1

a) The Probability that a single detection system will detect an attack = 0.95

b) P(X > 1) = P(X = 1) + P(X = 2)

                 = 2C1 * (0.95)^1 * (0.05)^1 + 2C2 * (0.95)^2 * (0.05)^0 = 0.9975

c) P(X > 1) = P(X = 1) + P(X = 2) + P(X = 3)

                  = 3C1 * (0.95)^1 * (0.05)^2 + 3C2 * (0.95)^2 * (0.05)^1 + 3C3 * (0.95)^3 * (0.05)^0

                  = 0.9999

d) No, we would not recommend that multiple detection systems be used, because the probability will be much higher.