We propose a notion of probabilistic proof for the multiplicative and additive fragment of linear logic (MALL) formulated in graphical (proof-nets) and sequential style (derivations). The definition of probabilistic proof is proved to be correct and complete with respect to the notion of Bayesian network that is a graphical model for representing joint probability distributions over a set of discrete (Boolean) random variables. Analogously to what happens with Bayesian networks, probabilistic proofs of linear logic are both an intelligible way of representing probabilities and an efficient method to reason about them.