The single shot probability of kill of any weapon system (gun, missle or slingshot) is less than 1 due to the reliability factors if no other reason. Suppose the single shot probability of kill of a new defensive missle system is 0.75%, and the the probability is not considered adequate. One familiar strategy to increase the overall probability of a defensive kill is to launch several defensive missiles at one incoming threat.
Let Pk (P underscore k) stand for the single shot probability of kill and Pt (P underscore t) stand for the overall probability of kill.
a) Develope a formula for the overall probability of kill, assuming that N defensive missles are launched.
b) You will have had to make a probabilistic assumption in order to develope the formula. What was that assumption?