National security requires that defense technology be able to detect incoming projectiles or missiles.
To make the defense system successful, multiple radar
screens are required. Suppose that three independent
screens are to be operated and the probability that any
one screen will detect an incoming missile is 0.8. Obviously, if no screens detect an incoming projectile, the
system is unworthy and must be improved.
(a) What is the probability that an incoming missile
will not be detected by any of the three screens?
(b) What is the probability that the missile will be detected by only one screen?
(c) What is the probability that it will be detected by at least two out of three screens?
