A Legal Mess

Much judicial commentary (and some professorial commentary) on the "doctrine of chances" fails to distinguish between

(i) the probability that a random selection of instances from some appropriate reference class will produce a conjunction of some specified states or values (e.g., "in instance 1 -- random draw number 1 --, event of type X occurs" and "in instance 2, event of type X [again] occurs" );

and

(ii) the probability, given a conjunction of of some specified states [such as in #(i)], that a criminal defendant caused those states of affairs.

Merely because the conjunction of events in situation #(i) above is highly improbable when instances of the reference class are chosen at random does not necessarily mean that some causal explanation -- such as "David Defendant caused such an improbable [i.e., rare] conjunction of events" -- is highly probable.

Why do legal professionals find it so hard to get a handle on the distinction between probabilities of type (i) and probabilities of type (ii)?

BTW: Does the following principle make intuitive sense to you?:

The occurrence of very improbable events and of very improbable combinations of events is highly probable.

Consider a restatement of this principle:

The occurrence of rare events and of rare sets of events is, over the long run [alternatively: "given a sufficiently large number of trials"], highly probable.