This paper considers a distributed formation control problem for a multi-agent system. The dynamic of agents is assumed to be Euler-Lagrange. An event-triggered approach is considered, leading to intermittent communications between agents. This paper addresses the situation where communications are prone to random packet losses. To evaluate its control input, each agent maintains multi-hypothesis estimators of its own state and of the states of its neighbors accounting for the potentially lost packets. Each agent is then able to compute the expected estimation error of its own state as evaluated by its neighbors. The condition to trigger communication (CTC) involves this expected error. An analysis of the behavior of the system with such CTC is performed using stochastic Lyapunov functions. Simulations confirm the effectiveness of the proposed approach.