The probability that the safety I&C system fails to actuate or advertently actuates RT or ESF functions, in part, essentially determines whether a nuclear power plant could operate safely and efficiently. Since more conservative assumptions and simplifications are introduced during the analysis, this paper achieves solid results by performing the modeling and calculation based on a relatively simple approach, the reliability block diagram (RBD) method. A typical safety I&C platform structure is involved in the model presented in this paper. From the perspective of conservation and simplicity, some assumptions are adopted in this paper. A group of formulas is derived in this paper based on Boolean algebra, probability theory, basic reliability concepts and equations, to facilitate the calculations of probabilities that the safety I&C system fails to actuate or advertently actuates RT or ESF functions. All the inputs of the analysis and calculation in this paper, which includes the I&C platform structure, the constitution of the hardware modules, and reliability data, are referenced to the nuclear power plant universal database where applicable. Although the conclusion drawn in the paper doesn't apply to the I&C platform assessment for a specific plant, the method of modeling and process of analysis provides an illustration of an alternative quantitative reliability assessment approach for a typical safety I&C system installed in the nuclear power plant.