In this paper, the problem of determining the probability of kill(or survival) of a vulnerable target by one or more missiles is considered. The general formulas are obtained for the kill or survival probability the target is killed or survival. Several well-known concepts such as those of vulnerability, lethality, multi-component target, and a general combinatorial theorem of probability are introduced and used. For the convenience in this paper, the word missile is used in a very general sense and the target is generally taken to be a point target. And, this paper, is concentrated primarily with the probabilistic aspects of the problem, also a general numerical procedures are also described. Two examples are shown to illustrate the use of some of the formulas in this study, but also illustrate a few points which may not have been sufficiently emphasized. The extension study to complete a software package will be followed.