The U.S. Air Force has designed a missile detection system which will detect 19 out of 20 incoming missiles. If one early warning system is good, two must be better; "how much better?".

a) What is the probability that 1 detection system will detect an incoming missile?

b) If 2 detection systems are installed in the same area and operate independently, what is the probability that at least 1 of the systems will detect the missile?

c) If 3 systems are installed, what is the probability that at least 1 of the systems detects the missile? 

d) How many detection systems would you recommend operating? Why?