We derive an explicit expression for the probability density of the amplitudes of the biexponential fluorescence decay of a two-state system observed in single-molecule experiments of finite duration T. The shape of the probability density of the amplitudes depends on (k(1) + k(2))T, where the k(i) are the interconversion rate constants. It approaches a delta function in the limit T --> infinity. When the interconversion rates in the ground and excited states differ, the single-molecule and bulk experiments will give different results even in the limit of infinite duration of the experiment.