In this paper, we propose a novel approach for solving the reliable broadcast problem in a probabilistic unreliable model. Our approach consists in first defining the optimality of probabilistic reliable broadcast algorithms and the adaptiveness of algorithms that aim at converging toward such optimality. Then, we propose an algorithm that precisely converges toward the optimal behavior, thanks to an adaptive strategy based on Bayesian statistical inference. We compare the performance of our algorithm with that of a typical gossip algorithm through simulation. Our results show, for example, that our adaptive algorithm quickly converges toward such exact knowledge.