The generation of random-like sequences is a common task for assessing high-level cognitive abilities, such as inhibition, sustained attention and working memory. In general, many studies have shown a detrimental effect of aging on pseudo-random productions. The performance of participants in random generation tasks has typically been assessed by measures of randomness such as, among others, entropy and algorithmic complexity that are calculated from the series of responses produced by the subject. We focus on analyzing the mental model of randomness that people implicitly use when producing random series. We propose a novel latent class model based on Markov chains that aims to classify individuals into homogeneous classes according to the way they generate head-tail series. Our results reveal that there are significant age-related differences in the way individuals produce random-like sequences. Specifically, the group of healthy adults implicitly uses a simpler mental mechanism, in terms of memory requirements, compared to the group of younger participants.