Probabilities for two properties

Let R(X, B) denote the class of probability functions that are defined on a lgebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is conc erned with characterizing R(X, B) for the case in which X is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which invo lve the notion of statistical dependence. The class of probability function s that satisfy these conditions, here denoted P_I, includes a class that Ca rnap once proposed for the same situation. Probability functions in P_I vio late Carnaps axiom of analogy but, it is argued, that axiom should be rejec ted. A derivation of Carnaps model by Hesse has limitations that are not pr esent in the derivation of P_I given here. Various alternative probability models are considered and rejected.