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 p. Obviously, if no screens detect an incoming projectile, the system is unworthy and must be improved.
In your solutions, let X be a random variable referring to the number of screens that will detect the incoming missile.
A. What must be the value of p such that the probability of NOT detecting an incoming missile by any of the three screens is less than 1% or 0.01? Round-off your answer to four (4) decimal places.
B. What must be the value of p such that there is a 99% chance that AT LEAST ONE of the screens detect an incoming missile? Round-off your answer to four (4) decimal places.