We present a fast data-driven model predictive control (MPC) strategy for connected and automated vehicles, which can ensure collision avoidance in the presence of uncertainty in shared/predicted trajectory of preceding vehicles. The proposed control strategy focuses on improvement in fuel economy and computational efficiency. We exploit a data-driven modeling approach to identify a linear predictor for the nonlinear system and evaluate a deterministic equivalent of the probabilistic collision avoidance constraint to formulate the equivalent convex optimal control problem. We then develop a hierarchical control framework with sampling-based high-level control and fast MPC-based low-level control. Simulation results show the efficacy of the proposed approach both in terms of computation time and fuel efficiency.