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The probability or risk of traffic accidents must be estimated quantitatively in order to implement effective traffic safety measures. In this study, various statistical data and probability theory were used to examine a method for predicting the risk of crossing-collisions, representing a typical type of accident at intersections in Japan. Crossing-collisions are caused by a variety of factors, including the road geometry and traffic environment at intersections and the awareness and intentions of the drivers of the striking and struck vehicles. Bayes' theorem was applied to find the accident probability of each factor separately. Specifically, the probability of various factors being present at the time of a crossing-collision was estimated on the basis of traffic accident data and observation survey data.