Brake System for a Vehicle and Method for Operating a Brake System for a Vehicle

A brake system includes a brake activation element, an activation-element-coupling device having a first piston which is moved into a first internal chamber of the activation-element-coupling device by activating the brake activation element, a master brake cylinder with a second piston to which a driver braking force is transmitted in a driver braking mode to move the second piston into a second internal chamber of the master brake cylinder, a braking medium reservoir, which is hydraulically disconnected from the second internal chamber when the second piston moves a minimum travel distance, and at least a first wheel brake cylinder and at least a first pump. In an external force braking mode, movement of the second piston is prohibited despite the driver's braking force, and the at least one first pump pumps a braking medium volume out of the braking medium reservoir into the at least one first wheel brake cylinder.