In the Slovenian National Mathematics Curriculum the probability contents are first mentioned in the ninth grade of elementary school (at the age of 14), yet they are introduced informally, only in some first triad textbook sets. The researchers disagree as to the age of children at which they are able to deal with certain probability contents. In view of this fact our aim was to establish the age at which children are able to differentiate among certain, possible and impossible events, and predict the likelihood of various events. 623 pupils of the first three grades of elementary school participated in the study. We presumed that they were able to differentiate among certain, possible and impossible events, and compare the probability of various events, while only half of the children aged 4-5 years participating in the research were equally able. The major difference in their abilities was noticed between the children aged from 4-5 years and the first graders, but there were only slight gender differences. Children of all age groups encountered difficulties at predicting events with equal probability. The first graders can be taught the latter by applying the teaching approach, based on their concrete experience, and by mastering the technique for solving tasks with equal probability. When comparing the results with the opinions of the respondent teachers and pre-school teachers, it is evident that they are under the misconception regarding the children's abilities to solve probability tasks. The majority of the respondents stated that children were able to differentiate among certain, possible and impossible events, and compare the probability of various events not earlier than at the age of eight years; on the contrary, the findings of our research established that children were able to achieve both goals much earlier. (Contains 4 figures and 6 tables.)