 Some of the difficulties of the former account are avoided. Necessary conditionals like “If \(A \amp B\), then \(A\)” are true—get value 1. Conjunctions of the form (if \(A, B)\) &amp; (if \({\sim}A, C)\) do not all get 0. Indeed, conditionals this form always get the value \(\mathbf{p}_A (B).\mathbf{p}_{{\sim}A}(C)\). (The expected value of the conjunction if \(\mathbf{p}(A \amp B).\mathbf{p}_{{\sim}A}(C) + \mathbf{p}({\sim}A \amp C).\mathbf{p}_A (B)\), which simplifies to \(\mathbf{p}_A (B).\mathbf{p}_{{\sim}A}(C)\).) Indeed, the stronger result holds, that if the two antecedents are incompatible, the value of the conjunction is the product of the two conditional probabilities. So our above example about rain, beach and cinema indeed gets a high value.