where "N"(drunk ∩ "D") denotes the number of drivers that are drunk and get a positive breathalyzer result, and "N"("D") denotes the total number of cases with a positive breathalyzer result. The equivalence of this equation to the above one follows from the axioms of probability theory, according to which "N"(drunk ∩ "D") = "N" × "p" ("D" | drunk) × "p" (drunk). Importantly, although this equation is formally equivalent to Bayes' rule, it is not psychologically equivalent. Using natural frequencies simplifies the inference because the required mathematical operation can be performed on natural numbers, instead of normalized fractions (i.e., probabilities), because it makes the high number of false positives more transparent, and because natural frequencies exhibit a "nested-set structure".