Missile Defense: Ukraine could use this system about now (30 points total)

The United States has developed a defense against ballistic missiles. The defensive system uses radars to identify and track incoming warheads and interceptors to destroy the warheads. The radars correctly identify and track 95% of all incoming warheads. If a warhead is properly identified and tracked, an interceptor has a 80% chance of destroying it.

a). A warhead is launched against the United States. What is probability that the warhead would be destroyed if only one interceptor is used?

b). Now suppose that up to three interceptors can be used. What is the probability that the warhead would penetrate the defense?

c). Suppose that five warheads are launched against the United States, and that the US can use up to three interceptors against each warhead. What is the probability that at least one warhead will penetrate the defense?