This paper develops a probabilistic model that can be used to determine the number of ballistic missile defense interceptors required to meet a specific defense objective, given the technical performance of the defense. The defense objective is stated as some probability that no warheads leak through the defense. The defense technical performance is captured by the interceptor single-shot probability of kill and the warhead detection, tracking, and classification probability. Attacks are characterized by the number of warheads and decoys that cannot be discriminated by the defense. Barrage and shoot-look-shoot firing modes are examined, with the optimal interceptor allocation derived for the shoot-look-shoot mode. Applications of this model to national and theater missile ballistic missile defense are discussed.