Single-molecule fluorescence spectroscopy can be used to estimate the rate constants for slow transitions between two states characterized by different lifetimes of a fluorescent probe.:The fluorescence decay for this system is a biexponential, the coefficients of each exponential being the fraction of time spent. by the system in each of the states.:This paper explains how to estimate the rate constants for the transitions and derives the sampling error for the estimates on the assumption that the data are gathered on M molecules, each monitored for a time T. Results of the analysis indicate that the dominant factor in determining the precision of the rate constant is M and that the role of T is less significant.