Rabin [21] initiated the study of probabilistic finite automata (PFA). Rabin’s work showed a crucial role of the gap in the error bound (for accepting and non-accepting computations) in the power of the model. Further work resulted in the identification of qualitatively different error models (one-sided error, bounded and unbounded errors, no error etc.) Karpinski and Verbeek [16] and Nisan [20] studied a model of probabilistic automaton in which the tape containing random bits can be read by a two-way head. They presented results comparing models with one-way vs. two-way access to randomness. Dwork and Stockmeyer [5] and Condon et al. [4] studied a model of 2-PFA with nondeterministic states (2-NPFA). In this paper, we present some results about the above mentioned variations of probabilistic finite automata, as well as a model of 2-PFA augmented with a pebble studied in [22]. Our observations indicate that these models exhibit subtle variations in their computational power. We also mention many open problems about these models. Complete characterizations of their power will likely provide deeper insights about the role of randomness is space-bounded computations.