What are the chances of a full recovery for a patient suffering fro a hypoxic brain injury?

Depends: Depends on how severe the hypoxic injury is, which is usually relative to the time the brain was deprived of oxygen, as well as to the patient's age and health condition. Full recovery is possible, especially with short hypoxic times and quick resuscitation. Talk to your doctors.

It depends: Brain cells do have a remarkable ability to recover. They can go into a shock state following hypoxia. With good support and good therapy many may recover and return to near normal function. Many may die. The outcome is hard to predict, but full effort is justified. At some point it will become obvious the degree of damage that has been done for which no recovery is possible.