1. A method for classifying a behavior of a pedestrian when crossing a roadway of a vehicle, the method comprising: reading in sensor signals, from surroundings sensors of the vehicle, to detect the pedestrian and at least one piece of surroundings information regarding surroundings of the pedestrian; ascertaining at least one physical variable of a relationship between the pedestrian and the at least one piece of surroundings information; classifying the behavior of the pedestrian using the at least one physical variable; determining at least one possible trajectory of the pedestrian as a function of the behavior of the pedestrian classified in the classifying; and providing an activation signal to activate at least one component of a passenger protection system of the vehicle as a function of the possible trajectory; wherein the passenger protection system includes: (i) an air-bag arrangement, and (ii) a pedestrian protection device having an automatic braking arrangement and an evasive maneuvering arrangement, and wherein the at least one component of the passenger protection system includes at least one of the automatic braking arrangement, the evasive maneuvering arrangement, and the air-bag arrangement.