Abstract: Nuclear reactor core damage is a possible severe accident during nuclear reactor operation. Based on the probabilistic safety assessment, the core damage frequency of a single nuclear reactor could be drawn. But concerning the probability of the number of core damage under the condition of multiple reactor years, it follows the binominal distribution. After calculation, with 10⁴ reactor years of operation and 10^-4 of core damage frequency, the probability of core damage is about 0.63.