For assessing toxic effects of mixtures, toxicologists developed the notion of “simple independent action (SIA).” [1]. The idea there was probabilistic independence. If there is no background risk, i.e. no risk in the absence of either exposure A or B, then the probability of avoiding an outcome, say D, when exposed to both A and B should be the product of the two separate avoidance probabilities. Under simple independent action, the risk factors A and B thus behave in a way that is mutually oblivious. A paradigm for this would be two duck hunters separately shooting at the same duck [2], where the duck must avoid the bullets coming from both. Violations of SIA would then indicate non-independence, which would be seen as synergy if the violation is in the direction of increased risk and antagonism if in the direction of reduced risk. An independently acting background cause (or aggregation of causes not including A or B) can be allowed for as yet another independently operating factor, so that if Pr[D | A,B] is the probability of D in the
