On the distribution of the number of walks until no shoes

This article presents a further analysis of the probabilistic problem known as The Number of Walks Until No Shoes, introduced by Blom et al. (1994). We show that, in the cases of one and two pairs of shoes, the distribution of the number of walks is given by a geometric random variable and by the sum of two independent geometric random variables, respectively. These results are intended for use as teaching material in early undergraduate courses to aid in the understanding of probability distributions.