Final answer:
Helium and argon are the two inert gases commonly used to purge flammable or explosive vapors from confined spaces due to their non-reactivity.
Step-by-step explanation:
The two inert gases often used to purge flammable or explosive vapors from a confined space are helium and argon. Helium is particularly known for its non-flammable property and its incapability to act as a narcotic under high pressures, making it a safe choice for applications such as filling balloons and as an inert atmosphere in diving mixtures to avoid nitrogen narcosis. Argon, another inert gas from the noble gas group, is commonly used due to its low reactivity for creating an inert atmosphere in welding and in light bulbs. Both gases are effective in displacing flammable gases and vapors due to their lack of reactivity, hence reducing the risk of combustion.