A missile defense system is intended to kill any incoming missiles directed at a country. The missile defense system has a successful-kill probability of 0.85 per attempt by the system. Assume that the attempts are independent,

(a) What is the probability that the kill will occur on the first attempt?

(b) What is the probability that the kill will occur on the second attempt?

(c) How many attempts are needed to achieve a successful kill with a probability of 0.99?

(e) Plot the number of attempts as a function of the probability in part

(c) over the probability range from 0.85 to 0.9999.