For long duration missions outside of the protection of the Earth's magnetic field, exposure to solar particle events (SPEs) is a major safety concern for crew members during extra-vehicular activities (EVAs) on the lunar surface or Earth-to-moon or Earth-to-Mars transit. The large majority (~90%) of SPEs have small or no health consequences because the doses are low and the particles do not penetrate to organ depths. However, there is an operational challenge to respond to events of unknown size and duration. We have developed a probabilistic approach to SPE risk assessment in support of mission design and operational planning. Using the historical database of proton measurements during the past 5 solar cycles, the functional form of hazard function of SPE occurrence per cycle was found for nonhomogeneous Poisson model. A typical hazard function was defined as a function of time within a non-specific future solar cycle of 4000 days duration. Distributions of particle fluences for a specified mission period were simulated ranging from its 5th to 95th percentile. Organ doses from large SPEs were assessed using NASA's Baryon transport model, BRYNTRN. The SPE risk was analyzed with the organ dose distribution for the given particle fluences during a mission period. In addition to the total particle fluences of SPEs, the detailed energy spectra of protons, especially at high energy levels, were recognized as extremely important for assessing the cancer risk associated with energetic particles for large events. The probability of exceeding the NASA 30-day limit of blood forming organ (BFO) dose inside a typical spacecraft was calculated for various SPE sizes. This probabilistic approach to SPE protection will be combined with a probabilistic approach to the radiobiological factors that contribute to the uncertainties in projecting cancer risks in future work