A Bayesian approach to solar flare prediction has been developed which uses only the event statistics of flares already observed. The method is simple and objective and makes few ad hoc assumptions. It is argued that this approach should be used to provide a baseline prediction for certain space weather purposes, upon which other methods, incorporating additional information, can improve. A practical implementation of the method for whole-Sun prediction of Geostationary Observational Environment Satellite (GOES) events is described in detail and is demonstrated for 4 November 2003, the day of the largest recorded GOES flare. A test of the method is described on the basis of the historical record of GOES events (1975--2003), and a detailed comparison is made with U.S. National Oceanic and Atmospheric Administration (NOAA) predictions for 1987--2003. Although the NOAA forecasts incorporate a variety of other information, the present method outperforms the NOAA method in predicting mean numbers of event days for both M-X and X events. Skill scores and other measures show that the present method is slightly less accurate at predicting M-X events than the NOAA method but substantially more accurate at predicting X events, which are important contributors to space weather.