This paper proposes and analyses the following theorem: For every total actual loss caused to a claimant with given probabilities by a single unidentified member of a defined group, there is a corresponding total expected loss, divisible and separable into discrete component expected sub-losses, each individually "caused" by a corresponding specific member of that defined group. Moreover, for every total estimated loss caused to a claimant in the past or present or prospectively in the future with estimable probabilities by one or more unidentified members or causal agents from a defined group, the same result holds. The theorem is applied to Mesothelioma compensation claims. It provides a new justification for the proportional apportionment rule in Barker v Corus 2006 and an explanation of some paradoxical consequences of the rule and of the rule's overall fairness.