The part of the brain that controls fine movement, maintains balance and equilibrium, and muscle tone in a human being is the cerebellum. Let`s understand each option to have a better understanding.

1) Cerebrum: The cerebrum is the largest part of the brain and is responsible for various higher-order functions such as thinking, memory, and sensation. However, it is not directly involved in controlling fine movement and balance.

2) Thalamus: The thalamus acts as a relay station for sensory information traveling to the cerebral cortex. It is involved in processing and relaying sensory signals, but it does not specifically control fine movement, balance, and muscle tone.

3) Cerebellum: The cerebellum, located at the back of the brain, is responsible for coordinating voluntary movements, balance, and muscle tone. It receives sensory information from the spinal cord and other parts of the brain and uses it to fine-tune and coordinate movements.

4) Hypothalamus: The hypothalamus is involved in regulating functions such as hunger, thirst, body temperature, and sleep cycles. It does not directly control fine movement, balance, and muscle tone.

Therefore, the correct answer is option 3, the cerebellum. It plays