For next 4 questions, use the following information: A missile protection system

Question

For next 4 questions, use the following information: A missile protection system consists of n radar sets operating independently, each with a probability .9 of detecting a missile entering a zone that is covered by all of the units.

Let X be the number of radar sets which detect an incoming missile. How is X distributed? Be sure to explain your answer.

If n=5 and a missile enters the zone, what is the probability that exactly 4 sets detect it?

If n=5 and a missile enters the zone, what is the probability that at least 1 set detects it?

What is the expected proportion of missile sets that will detect an incoming missile when n=20?

Explanation / Answer

X is a binomial distribution as the events are either detecting or not detecting and the probability of events doesnt change

probability that exactly 4 sets detect it = 5C4 x 0.94 x0.1 = 0.328

probability that at least 1 set detects it = 1 - probability of none detecting

= 1 - 0.15 = 0.99999

when n = 20,  expected proportion of missile sets that will detect an incoming missile = np = 0.9x20 = 18

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