Final answer:
The correct pairing is 'A) REM sleep - Rapid eye movements, vivid dreaming,' where REM sleep features active brain waves similar to those during wakefulness, rapid eye movements, and vivid dreams.
Step-by-step explanation:
The correct pairing of a sleep stage with its corresponding brain activity is A) REM sleep - Rapid eye movements, vivid dreaming. During REM sleep, brain waves are very similar to wakefulness, and this is the stage where dreaming typically occurs. As stated in the reference material, REM sleep exhibits brain waves that are highly active, resembling those when a person is awake, and it includes rapid eye movements and muscle paralysis, with the exception of the muscles that facilitate respiration and circulation.
In contrast, Stage 1 sleep is characterized by both alpha and theta waves and is a transitional period where we drift off to sleep, not deep sleep with delta waves as described in option B. Stage 2 sleep includes theta waves and is marked by sleep spindles and K-complexes, not only light sleep as mentioned in option C. Lastly, Stage 3 sleep is deep sleep characterized by low-frequency, high-amplitude delta waves, not by alpha waves which are related to wakefulness and transition into sleep as suggested in option D.