We propose a robust event-triggered model predictive control (MPC) scheme for linear time-invariant discrete-time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state. For given probability distributions of the disturbances acting on the system, we design event conditions such that the average frequency of communication between the controller and the actuator in the closed-loop system attains a given value. We employ Tube MPC methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state. Moreover, we show that instead of a given periodically updated Tube MPC scheme, an appropriate event-triggered MPC scheme can be applied, with the same guarantees on constraints and region of attraction, but with a reduced number of average communications.