2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169844This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval [p/μ_2, pμ_1], with μ_1, μ_2 > 1, is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper, and for any value of p. This extends the applicability of the estimator, relaxing the conditions that guarantee a given confidence level.2 figures. Paper accepted in IEEE Transactions on CommunicationsComputationtext