Wireless communication among connected and automated vehicles (CAVs) enables cooperative driving, particularly using cooperative adaptive cruise control, hence allowing CAVs to safely move closer to each other and improving traffic flow. However, reducing the gap between vehicles may cause collision, especially when a sudden deceleration in the vehicle platoon occurs. Furthermore, if some of the CAVs in the platoon lose communication, even for a short period, they may detect sudden changes in traffic with delay, and their reaction to avoid collision could be unsuccessful. Hence, an efficient emergency braking system can help preserve safety. This becomes even more important in high-speed driving, where a crash can put human lives in danger. This paper presents a discrete hybrid stochastic model predictive control approach to achieve a safe and efficient traffic system through CAV platooning. Three operational modes for vehicles are considered: free following, warning, and emergency braking. Each CAV in the free-following mode basically follows its preceding vehicle while enforcing maximum allowable deceleration in the emergency-braking mode. In the warning mode, the vehicle aims to slightly increase its headway and velocity difference from its predecessor to avoid possible danger. The warning/emergency-braking mode may be activated when the speed difference between a CAV and its preceding vehicle drops below a threshold. It is further assumed that vehicle distance sensing is subject to error. Each vehicle shares its current location, velocity, and future acceleration profile, calculated by solving a mixed-integer programming problem, with its follower vehicles. Simulation studies demonstrate the efficacy of the proposed control design approach compared to existing controllers in the literature in the presence of intermittent communication.