Infants have been described as 'statistical learners' capable of extracting structure (such as words) from patterned input (such as language). Here, we investigated whether prior knowledge influences how infants track transitional probabilities in word segmentation tasks. Are infants biased by prior experience when engaging in sequential statistical learning? In a laboratory simulation of learning across time, we exposed 9- and 10-month-old infants to a list of either disyllabic or trisyllabic nonsense words, followed by a pause-free speech stream composed of a different set of disyllabic or trisyllabic nonsense words. Listening times revealed successful segmentation of words from fluent speech only when words were uniformly disyllabic or trisyllabic throughout both phases of the experiment. Hearing trisyllabic words during the pre-exposure phase derailed infants' abilities to segment speech into disyllabic words, and vice versa. We conclude that prior knowledge about word length equips infants with perceptual expectations that facilitate efficient processing of subsequent language input.