Conditioning on a variable is not the same thing as intervening to fix the value of a variable, and the conditional probability of y given some particular value of x is not the same thing as the probability of y conditional on an intervention that “sets” this value of x. When one conditions, one takes as given the probability distribution. When one intervenes, one changes the probability distribution (but see pp. 229–30). These observations suggest a problem. The difference in the probability of b with and without an intervention that brings about a seems a surer guide to causal relations than does a comparison of Pr(B/A) and Pr(B/∼A). Do attempts to reduce causation to facts about probability distributions or merely to operationalize them in those terms rest on a confusion of conditional probabilities and probabilities given interventions? Do they collapse when this distinction is drawn? For example, suppose (as Ronald Fisher hypothesized) that tokens of smoking, s, and lung cancer, c, are related as effects of some common cause and not as cause and effect. In that case, even though Pr(C/S) > Pr(C/∼S), the probability of lung cancer is unaffected by interventions that bring about or prevent smoking. Following Pearl (1993, p. 267; 1995, p. 673), let us indicate the conditional probability that B will be instantiated given an intervention that brings about a token of kind a as Pr(B/set-A) and the conditional probability that y = y* given an intervention that causes the value of x to be x* as Pr(y=y*/set-x=x*) or less precisely as Pr(y/set-x).