In this research work we explored the nature of 9-12 year old pupils' responses to probabilistic problems with tree diagrams. It was found that a large percentage of pupils failed to respond correctly even to very simple problems that demanded the identification of "possible routes/paths" in figures with tree diagrams/mazes. The results also revealed the existence of subjective elements and other errors in pupils' thinking. The data were generated in year 2000 when the new mathematics books were introduced extensively in the primary schools. Comparisons are done by age and gender. The results of the study form a general overview and build the basis for further and more focused research because the relevant literature, especially regarding Cyprus, is very sparse. (Contains 2 figures and 3 tables.) [For complete proceedings, see ED500858.]