This paper studies the consensus problem of the switched multi-agent system composed of continuous-time and discrete-time subsystems. Communication among agents is modelled as a random network where the existence of any information channel is probabilistic and independent of other channels. Then, some necessary and sufficient conditions are presented for solving average consensus of the switched multi-agent system under arbitrary switching. Furthermore, we show that the average consensus in different sense (mean square, almost surely and in probability, respectively) are equivalent. Finally, simulations are provided to illustrate the effectiveness of our theoretical results.