We propose a new class of probabilistic neural-symbolic models, that have symbolic functional programs as a latent, stochastic variable. Instantiated in the context of visual question answering, our probabilistic formulation offers two key conceptual advantages over prior neural-symbolic models for VQA. Firstly, the programs generated by our model are more understandable while requiring less number of teaching examples. Secondly, we show that one can pose counterfactual scenarios to the model, to probe its beliefs on the programs that could lead to a specified answer given an image. Our results on the CLEVR and SHAPES datasets verify our hypotheses, showing that the model gets better program (and answer) prediction accuracy even in the low data regime, and allows one to probe the coherence and consistency of reasoning performed.