A missile protection system consists of n radar sets operating independently, each with a probability of 0.7 of detecting a missile entering a zone that is covered by all of the units.
a) If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? Round the answer to 3 decimals.
b) If n = 5 and a missile enters the zone, what is the probability that at least two sets detect the missile? Round the answer to 3 decimals.
c) How large must n be if we need the probability of detecting the missile by at least one set of radar to be at least 0.999?
Hint: Let X be the number of radar sets that detect the missile. Does X follow a special probability distribution?