This paper presents a framework for computing successful decoding probability of random network coding (RNC) in wireless networks. As cooperation emerges due to the naturally occurring broadcasting in wireless links, the application of RNC in wireless networks enables random network coded cooperation (RNCC). The theoretical successful decoding probability of RNCC systems is derived by obtaining the ratio of the full rank and the rank deficient matrices. The full rank condition of the global encoding matrix indicates the successful decoding of source symbols. The results of a single relay along with a relay selection scheme are also investigated. The validity of the presented theoretical expressions is demonstrated through identical simulation results. An implementation scenario is also presented to demonstrate the practical usage effectiveness of RNC in real-time applications, by using software-defined radio nodes.