This assertion of irrelevance translates into a symbolic manipulation: P(Y | do(X), Z, W) = P(Y | do(X), Z) The stated equation holds provided that the variable set Z blocks all the paths from W to Y after we have deleted all the arrows leading into X. In the example of Fire → Smoke → Alarm, we have W = Fire, Z = Smoke, Y = Alarm, and Z blocks all the paths from W to Y. (In this case we do not have a variable X.)
