 states that if the probability of \(\phi \wedge \psi\) is \(a\) and the probability of \(\phi\wedge \neg \psi\) is \(b\), then the probability of the disjunction of the formulas (which is equivalent to \(\phi\)) is \(a+b\). However, while the use of linear combinations allows us to assert that the probabilities of \(\varphi\wedge\psi\) and \(\varphi\wedge\neg\psi\) are additive by using the formula \(P(\varphi\wedge \psi)+P(\varphi\wedge\neg\psi) = P(\varphi)\), the formula without linear combinations above only does so if we choose the correct numbers \(a\) and \(b\). A formal comparison of the expressiveness of propositional probability logic with linear combinations and without is given in Demey and Sack (2015). While any two models agree on all formulas with linear combinations if and only if they agree on all formulas without (Lemma 4.1 of Demey and Sack (2015)), it is not the case that any class of models definable by a single formula with linear combinations can be defined by a single formula without (Lemma 4.2 of Demey and Sack (2015)). In particular, the class of models defined by the formula \(P(p)- P(q)\ge 0\) cannot be defined by any single formula without the power of linear combinations.