Final answer:
Damage to the right hemisphere of the brain is most likely to result in a failure to recognize one's own limbs, as this hemisphere is responsible for processing sensory information and spatial awareness.
Step-by-step explanation:
A failure to recognize that one's arm or leg is part of one's self is most likely to be associated with damage to the right hemisphere of the brain. This phenomenon is known as somatoparaphrenia and is often caused by damage to the parietal lobes of the right hemisphere, which are involved in processing sensory information and spatial awareness.
The left hemisphere, in comparison, is typically associated with language abilities in the majority of the population. The descending neural connections cross in the brainstem, meaning that the left hemisphere controls the right side of the body and vice versa.