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

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?

## Answers ( )

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