There are YouTube videos where a person hold a cup of $\rm CO_2$ and pour it on top of burning candles to distinguish them. As far as I know, $\rm CO_2$ and $\rm O_2$ both are almost perfect ideal gas at atmospheric conditions, so the volume they occupy shouldn't affect each other. Their joint probability distribution should just be the two Boltzmann distributions in product, and should be mostly uncorrelated. If so, how can $\rm CO_2$ displace $\rm O_2$ and distinguish fire?

While a cup of CO2 has partial pressure much higher than CO2 partial pressure in the atmosphere, I feel it should still be nearly ideal since N2 is nearly ideal even though the atmosphere is almost all N2 (same order of magnitude)