Final answer:
The brightness's of the remaining light bulbs stay the same when one of the light bulbs is removed from the circuit and replaced with a wire of zero resistance in a series circuit.
Step-by-step explanation:
When light bulbs are connected in series and one of them is chosen at random, removed from the circuit, and replaced with a wire of zero resistance, the brightness's of the remaining light bulbs remain the same.
In a series circuit, the same current flows through each component. Therefore, removing a light bulb and replacing it with a wire of zero resistance does not change the current or voltage in the circuit. As a result, the brightness of the remaining light bulbs does not change.