2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62708We consider the classical one-dimensional random walk of a particle on the right-half real line. We assume that the particle is initially at position x=k, k > 0, and moves to the right with probability p or to the left with probability 1-p. We consider that the particle is absorbed at the origin without fixing the number of steps needed to get there. We calculate the probability P(x=k) that the particles end up at the origin, given that it starts at x=k, by means of a geometric representation of this random walk in terms of paths on a two-dimensional lattice.latex 8 pages, 4 figuresProbability82B41text