This paper presents the first Monte Carlo simulation of binary stars in dwarf spheroidal galaxies that explores the effect of varying the distributions of the orbital parameters on the observed velocity dispersion. Our approach enables us to estimate the percentage of binary stars that would be recognized as such over the course of repeated observations. From the results presented here, it is possible to assess the relative merits of repeated observations and smaller measuring errors when trying to detect binary stars. In order to make these calculations, a more general method has been adopted than methods used previously. Using the method presented in this paper it should be possible for all observers of stars in dwarf spheroidal (dSph) galaxies to compare the numbers of binary stars that they have observed with any distribution of parameters for the binary orbits. Our conclusion is that for orbital distributions similar to those measured for the solar neighbourhood, the contribution of binary stars to the velocity dispersion is small. The number of binary stars that have been detected by observers of dwarf spheroidal galaxies is also consistent with these distributions. The truth of this latter conclusion is, however, dependent on the exact size of the measuring errors and the number of years over which observations have been made. Orbital parameters, very different from those measured for the solar neighbourhood, would be required for the binary stars to be making a significant contribution to the velocity dispersions that have been measured for dSph galaxies. In particular more smaller period orbits with higher mass secondaries would be required. The shape of the velocity distribution may help to resolve this issue when more data become available since, in general, the scenarios producing a larger apparent dispersion have a velocity distribution that deviates more clearly from Gaussian.