A missile protection system consists of n radar sets operating independently, each with probability 0.9 of detecting a missile entering a zone that is covered by all of the units. a) Find a nice expression for the probability of detecting at least one of the sets detects the missile. (Tip: what is the probability, that a missile is not detected by any of the sets? - and what has this probabilityto do with the above?) b) How large must n be if we require that the probability of detecting a missile that enters the zone be 0.999? 0.999999? c) If n = 5 and a missile enters the zone, what is the probability that exactly 4 sets detect the missile? At least one set?

Question

Douglas Spears

Mathematics

15 April, 19:53

A missile protection system consists of n radar sets operating independently, each with probability 0.9 of detecting a missile entering a zone that is covered by all of the units. a) Find a nice expression for the probability of detecting at least one of the sets detects the missile. (Tip: what is the probability, that a missile is not detected by any of the sets? - and what has this probabilityto do with the above?) b) How large must n be if we require that the probability of detecting a missile that enters the zone be 0.999? 0.999999? c) If n = 5 and a missile enters the zone, what is the probability that exactly 4 sets detect the missile? At least one set?

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Answers (1)

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Alissa Carey · Answer 1

A.) The probability that the missile is not detected by any of n sets = (1-0.9) ^n = 0.1^n.

Where it's opposite will be that the missile is detected by atleast 1 of the sets. Which will be equals to 1 - (0.1) ^n.

B.) 0.999 = 1 - (0.1) ^n

Here n=3

For, 0.999999=1 - (0.1) ^n

n=6.

C.) If n=5

5C4 * (0.9) ^4 * (0.1) ^1 = 0.32805