For future space missions outside of the Earth's magnetic field, the risk of radiation exposure from solar particle events (SPEs) during extra-vehicular activities (EVAs) or in lightly shielded vehicles is a major concern when designing radiation protection including determining sufficient shielding requirements for astronauts and hardware. While the expected frequency of SPEs is strongly influenced by solar modulation, SPE occurrences themselves are chaotic in nature. We report on a probabilistic modeling approach, where a cumulative expected occurrence curve of SPEs for a typical solar cycle was formed from a non-homogeneous Poisson process model fitted to a database of proton fluence measurements of SPEs that occurred during the past 5 solar cycles (19-23) and those of large SPEs identified from impulsive nitrate enhancements in polar ice. From the fitted model, we then estimated the expected frequency of SPEs at any given proton fluence threshold with energy >30 MeV (Phi(30)) during a defined space mission period. Analytic energy spectra of 34 large SPEs observed in the space era were fitted over broad energy ranges extending to GeV, and subsequently used to calculate the distribution of mGy equivalent (mGy-Eq) dose for a typical blood-forming organ (BFO) inside a spacecraft as a function of total Phi(30) fluence. This distribution was combined with a simulation of SPE events using the Poisson model to estimate the probability of the BFO dose exceeding the NASA 30-d limit of 250 mGy-Eq per 30 d. These results will be useful in implementing probabilistic risk assessment approaches at NASA and guidelines for protection systems for astronauts on future space exploration missions.