A normal sequence over {0,1} is an infinite sequence for which every word of length k appears with frequency 2^{−k}. Agafonov’s eponymous theorem states that selection by a finite state selector preserves normality, i.e. if α is a normal sequence and A is a finite state selector, then the subsequence A(α) is either finite or a normal sequence. In this work, we address the following question: does this result hold when considering probabilistic selectors? We provide a partial positive answer, in the case where the probabilities involved are rational. More formally, we prove that given a normal sequence α and a rational probabilistic selector P, the selected subsequence P(α) will be a normal sequence with probability 1.