 The difference between the probability distributions resulting from conditioning and from intervening is formally represented by supplementing the probability calculus with the do-operator (\(\do(X)\)) where applying the operator to a variable formally represents intervening upon it. Taking \(T\), \(S\), and \(M\) to denote Treatment, Success, and Gender, and given the graph in  Figure 2,   the observational probability distribution of \(S\) given \(T\) is not equal to the probability distribution of \(S\) given an intervention on \(T\): 