Molecular noise is a natural phenomenon that is inherent to all biological systems^,. How stochastic processes give rise to the robust outcomes that support tissue homeostasis remains unclear. Here we use single-molecule RNA fluorescent in situ hybridization (smFISH) on mouse stem cells derived from haematopoietic tissue to measure the transcription dynamics of three key genes that encode transcription factors: PU.1 (also known as Spi1), Gata1 and Gata2. We find that infrequent, stochastic bursts of transcription result in the co-expression of these antagonistic transcription factors in the majority of haematopoietic stem and progenitor cells. Moreover, by pairing smFISH with time-lapse microscopy and the analysis of pedigrees, we find that although individual stem-cell clones produce descendants that are in transcriptionally related states—akin to a transcriptional priming phenomenon—the underlying transition dynamics between states are best captured by stochastic and reversible models. As such, a stochastic process can produce cellular behaviours that may be incorrectly inferred to have arisen from deterministic dynamics. We propose a model whereby the intrinsic stochasticity of gene expression facilitates, rather than impedes, the concomitant maintenance of transcriptional plasticity and stem cell robustness.