This paper reports on a study that investigated young children's responses to a range of probabilistic tasks. A central aspect of the study was our examination of the children's use of subjective thinking. Most research that has been conducted in relation to young children's probabilistic thinking has focused on the extent to which young children can identify the most and least likely outcome of experiments. There is, however, limited research into the types of judgements children use when making these identifications. For example, while a small number of studies have reported on children's use of subjective thinking, there is an absence of research focusing on the role of subjectivity and the range of beliefs on which these judgements are based. In this research, the subjective thinking of children aged 5-6 years in Ireland was examined to address this gap in current knowledge. The data were collected through task-based group interviews and analysed using thematic analysis. Results suggest that a range of personal beliefs and experiences influence young children's probabilistic thinking including the physical position of objects, personal affinity for one possible outcome, a desire to win, and the influence of previous experiments.