Abstract: The probabilistic combination method is a very useful method to analyze the reliability of wireless sensor network (WSN), and it can effectively deal with the isolation effect and competition failure in the network. However, there are some shortcomings in the reliability modeling and calculation of WSN based on the probabilistic combination method in the existing literature, which leads to a limited application of the research results and even an incorrect evaluation for the reliability of WSN. This paper studies the reliability modeling and calculation of a typical WSN which has only one relay node and the probabilistic functional dependence mechanism. Under the general assumption that WSN faces local failures of components and global failures caused by external attacks, a reliability model that is more realistic and more rigorous is established for WSN. Based on rigorous probability combination analysis, it shows systematic method and compact formulas for the reliability of WSN. The current study enhances the research on such issues in the literature efficiently. Finally, as applications, we calculate the reliability of two special WSNs ---body sensor network and air monitoring system.