This article presents a novel stochastic event-based super-twisting controller design for addressing the formation control problem in the networked multiagent system in the presence of an external disturbance. The stochasticity in the system is introduced by randomness of network uncertainties, i.e., losses and delays of data packets. The proposed design has three parts. The first part derives an event-triggering condition for control input updates of each agent in the system. The second part guarantees desired formation in finite time by deriving an upper bound on reaching time to the designed sliding surface of each agent. The third part ensures admissibility of event-based control updates of the agents such that they achieve stable desired formation. The proposed stochastic design has been validated on Pioneer P3-DX mobile robots. The results show the three-fold effectiveness of stochastic design. They are: 1) retaining the advantages of event-triggering strategy; 2) retaining the advantages of super-twisting sliding-mode controller; and 3) robust toward network uncertainties.