We use quantitative uncertainty analysis techniques to estimate the likelihoods of climate change in the 21st century. We use the Latin Hypercube approach to perform a Monte-Carlo simulation based on uncertainty in eight factors determining anthropogenic emissions projections and three climate model properties. Although uncertainty in the emission model's factors are assessed via expert judgment, uncertainty in the climate system properties can now be constrained by climate observations of the 20th century. By sampling from the uncertain input distributions and running approximately 500 simulations with the MIT Integrated Global System Model, this method produces probability distributions for temperature and sea level change in the 21st century. We present results from two cases, with and without mitigation policies, to demonstrate the effect on the probability distribution of climate change. As an illustration of the approach we find that, absent mitigation policies, our median projection shows a global mean surface temperature rise from 1990 to 2100 of 2.3 degrees C, with a 95 percent confidence interval of 0.9 to 5.3 degrees C. With a strong policy applied (a so called Beyond Kyoto case), the 95 percent confidence interval is reduced to 0.5 to 2.5 degrees C with a median of 1.4 degrees C. Probability distributions for sea level and other climate model variables will also be presented.