Extreme space weather events are low-frequency, high-risk phenomena. Estimating their rates of occurrence, as well as their associated uncertainties, is difficult. In this study, we derive statistical estimates and uncertainties for the occurrence rate of an extreme geomagnetic storm on the scale of the Carrington event (or worse) occurring within the next decade. We model the distribution of events as either a power law or lognormal distribution and use (1) Kolmogorov-Smirnov statistic to estimate goodness of fit, (2) bootstrapping to quantify the uncertainty in the estimates, and (3) likelihood ratio tests to assess whether one distribution is preferred over another. Our best estimate for the probability of another extreme geomagnetic event comparable to the Carrington event occurring within the next 10 years is 10.3% 95%  confidence interval (CI) [0.9,18.7] for a power law distribution but only 3.0% 95% CI [0.6,9.0] for a lognormal distribution. However, our results depend crucially on (1) how we define an extreme event, (2) the statistical model used to describe how the events are distributed in intensity, (3) the techniques used to infer the model parameters, and (4) the data and duration used for the analysis. We test a major assumption that the data represent time stationary processes and discuss the implications. If the current trends persist, suggesting that we are entering a period of lower activity, our forecasts may represent upper limits rather than best estimates.