Note that random_member/2 doesn't backtrack like member/2 does. To achieve enumerating the list in random order, one can use something like random_permutation([1,2,3], R), member(X, R).

Doc needs help

Typo:

Fails of List is the empty list.

to

Fails if List is the empty list.

This needs either a throw or a fix

This is not good (well, it it if you want to use random_member/2 to generate a stream of random booleans, but I think that's taking nondeterminism too far):

?- random_member(1,[1,2,3]).
false.

?- random_member(1,[1,2,3]).
true.

random_member(1,[1,2,3]) should succeed because 1 is, if not a "random" member, then at least a member of [1,2,3]