 denotes the conditional probability of X on condition Y, \(\overline{C}\) denotes the absence of event C (the negation of the proposition that C happens) and it is assumed that neither C nor \(\overline{C}\) has probability zero. Line (2) says that A and B are conditionally independent, given C. In Reichenbach’s terminology, C screens A off from B. Line (3) says that \(\overline{C}\) also screens A off from B. Lines (4) and (5) say that A and B are more probable, conditional on C, than conditional on the absence of C. These inequalities are natural consequences of C being a cause of A and of B. Together, conditions (2) through (5) mathematically entail  (1).  The common cause can thus be understood to explain the correlation in (1). The probability relations described in lines (1) through (3) exhibit a version of Simpson’s Paradox. For more about this probabilistic phenomenon, see the entry on  Simpson’s Paradox.