What does it mean for one event C to cause another event E for example, smoking (C) to cause cancer (E)? There is a long history in philosophy, statistics, and the sciences of trying to clearly analyze the concept of a cause. One tradition says that causes raise the probability of their effects; we may write this symbolically is(|)>().

Does equation (1) imply that (|)>()P(C|E)>P(C)? If so, prove it. If not, give a counter example.