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When considering a patient with a lesion in the left basal ganglia, it is essential to understand the anatomy and functional organization of the basal ganglia as well as the nature of motor control and associated symptoms.

Lesions in the left basal ganglia can impair movement control on the opposite side of the body due to the crossover of pathways in the nervous system. In this case, an injury in the left basal ganglia would lead to symptoms manifesting in the right extremities.

The presence of cogwheel rigidity and tremor indicates a dysfunction typically associated with conditions such as Parkinson's disease, a common complication of basal ganglia lesions. Cogwheel rigidity is characterized by a ratchety resistance during passive movement, which reflects the underlying basal ganglia pathology where both inhibition and excitation of motor pathways are disrupted. In addition, a tremor, which can be resting, is a common symptom when basal ganglia function is compromised.

Thus, the observed symptoms of cogwheel resistance to passive range of motion and tremor in the right extremities align with the expected clinical presentation resulting from a left basal ganglia lesion. This understanding of basal ganglia pathology and its clinical implications provides clarity on why these symptoms are the most likely to be observed.