 FC can fail if the probabilistic parameters in a causal model are just so. In  Figure 8,  for example, X influences Z along two different directed paths. If the effect of one path is to exactly undo the influence along the other path, then X and Z will be probabilistically independent. If the underlying SEM is linear, Spirtes et al. (SGS 2000: Theorem 3.2) prove that the set of parameters for which Faithfulness is violated has Lebesgue measure 0. Nonetheless, parameter values leading to violations of FC are possible, so FC does not seem plausible as a metaphysical or conceptual constraint upon the connection between causation and probabilities. It is, rather, a methodological principle: Given a distribution on \(\{X, Y, Z\}\) in which X and Z are independent, we should prefer the causal structure depicted in  Figure 7  to the one in Figure 8. This is not because Figure 8 is conclusively ruled out by the distribution, but rather because it is preferable to postulate a causal structure that implies the independence of X and Z rather than one that is merely consistent with independence. See Zhang and Spirtes 2016 for comprehensive discussion of the role of FC.