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The intelligent reflective surface (IRS) technology has received many interests in recent years, thanks to its potential uses in future wireless communications, in which one of the promising use cases is to widen coverage, especially in the line-of-sight-blocked scenarios. Therefore, it is critical to analyze the corresponding coverage probability of IRS-aided communication systems. To our best knowledge, however, previous works focusing on this issue are very limited. In this paper, we analyze the coverage probability under the Rayleigh fading channel, taking the number and size of the array elements into consideration. We first derive the exact closed-form of coverage probability for the unit element. Afterward, with the method of moment matching, the approximation of the coverage probability can be formulated as the ratio of upper incomplete Gamma function and Gamma function, allowing an arbitrary number of elements. Finally, we comprehensively evaluate the impacts of essential factors on the coverage probability, such as the coefficient of fading channel, the number and size of the element, and the angle of incidence. Overall, the paper provides a succinct and general expression of coverage probability, which can be helpful in the performance evaluation and practical implementation of the IRS.