A philosophical question on probability theory This question is philosophical in nature. The example is taken from theology, but one may invent more examples, including these more scientific than mine. Nevertheless it is a valid mathematical issue. Accordingly (my understanding of) Protestant theology: 1. Salvation of a human does not directly depend on his deeds, because salvation is by faith only. 2. But salvation "indirectly" depends on deeds: salvation depends on faith and deeds also depend on faith. Or replacing the concrete question with more abstract one: 1. A does not directly depend on B. 2. But A indirectly depends on B: A depends on C and B also depend on C. I ask you to formalize in terms of probability theory (or some other kind of logic) these my informal musings.

In a draw of a card from a deck, let A be to draw a spade and B to draw a king. Then A does not depend on B, in fact A,B are independent. However if C were say to draw the queen of spades, then each of A and B would definitely depend on C.