B) Cerebellum
The cerebellum, a part of the hind-brain, is responsible for precision of voluntary actions and maintaining posture and balance of the body.
Source: Chapter 6, Section 6.1.2 Human Brain
The textbook explicitly states: "a part of the hind-brain called the cerebellum… is responsible for precision of voluntary actions and maintaining the posture and balance of the body." Do not confuse cerebellum (precision/balance) with cerebrum/fore-brain (thinking/voluntary initiation) or medulla (involuntary actions like blood pressure, vomiting).