A missile protection system consists of n radar sets operating independently, each with probability 0.9 of detecting a missile entering a zo

Question

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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Vivian 2 weeks 2022-01-06T05:59:04+00:00 1 Answer 0 views 0

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    2022-01-06T06:00:49+00:00

    Answer:

    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

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