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The main objective of the study is to determine the probability distributions of the geomagnetic Dst index as a function of the coronal mass ejection (CME) and solar flare parameters for the purpose of establishing a probabilistic forecast tool for the intensity of geomagnetic storms. We examined several CME and flare parameters as well as the effect of successive CME occurrence in changing the probability for a certain range of Dst index values. The results confirm some previously known relationships between remotely observed properties of solar eruptive events and geomagnetic storms: the importance of the initial CME speed, apparent width, source position, and the class of the associated solar flare. We quantify these relationships in a form that can be used for future space-weather forecasting. The results of the statistical study are employed to construct an empirical statistical model for predicting the probability of the geomagnetic storm intensity based on remote solar observations of CMEs and flares. [ABSTRACT FROM AUTHOR]