Organogenesis relies on the spatiotemporal balancing of differentiation and proliferation driven by an expanding pool of progenitor cells. In the mouse pancreas, lineage tracing at the population level has shown that the expanding pancreas progenitors can initially give rise to all endocrine, ductal, and acinar cells but become bipotent by embryonic day 13.5, giving rise to endocrine cells and ductal cells. However, the dynamics of individual progenitors balancing self-renewal and lineage-specific differentiation has never been described. Using three-dimensional live imaging and in vivo clonal analysis, we reveal the contribution of individual cells to the global behaviour and demonstrate three modes of progenitor divisions: symmetric renewing, symmetric endocrinogenic, and asymmetric generating a progenitor and an endocrine progenitor. Quantitative analysis shows that the endocrine differentiation process is consistent with a simple model of cell cycle-dependent stochastic priming of progenitors to endocrine fate. The findings provide insights to define control parameters to optimize the generation of beta-cells in vitro.