 Call a set of mutually exclusive and jointly exhaustive propositions a partition. The lines of a truth table constitute a partition. One’s degrees of belief in the members of a partition, idealized as precise, should sum to 100%. That is all there is to the claim that degrees of belief should have the structure of probabilities. Consider a partition of the form \(\{A \amp B, A \amp{\sim}B, {\sim}A\}\). Suppose someone X thinks it 50% likely that \({\sim}A\) (hence 50% likely that \(A), 40\)% likely that \(A \amp B\), and 10% likely that \(A \amp{\sim}B\). Think of this distribution as displayed geometrically, as follows. Draw a long narrow horizontal rectangle. Divide it in half by a vertical line. Write “\({\sim}A\)” in the right-hand half. Divide the left-hand half with another vertical line, in the ratio 4:1, with the larger part on the left. Write “\(A \amp B\)” and “\(A \amp{\sim}B\)” in the larger and smaller cells respectively.