A theoretical framework is presented that connects "classic" fluorescence correlation spectroscopy (FCS) treating averages of many freely diffusing molecules and FCS single-molecule analysis. By assuming a general two-state emission dynamics of the single molecule, expressions describing the autocorrelation of the total fluorescence fluctuations are derived. By studying an idealized experimental situation, the relation between signal-to-noise and signal-to-background ratios are discussed. Under appropriate conditions it is possible to make statistically feasible measurements of single molecule dynamics despite low signal-to-background. The quantum yield ratio of the background molecules to the single molecule as well as the position of the single molecule inside the detection volume are crucial in obtaining good signal-to-noise ratios in single-molecule experiments.