Final answer:
The group contingency described is an interdependent group contingency, where the entire class receives a reward based on the action of a randomly chosen individual.
Step-by-step explanation:
The type of group contingency described in the scenario is known as an interdependent group contingency. This strategy involves providing a common reward to an entire group based on the behavior or performance of a single member or a subset of the group. In the scenario provided, the teacher has indicated that everyone in the class will receive extra recess if a randomly chosen student has completed and brought back their math homework. The contingency does not only depend on individual performance but rather on the selected student's action affecting the entire group, thus promoting group responsibility and peer support for completing homework.