  Reichenbach defined a common cause which explains a correlation between two
events if either one does not cause the other. Its intuitive idea is that the
statistical ensemble can be divided into two disjoint parts so that the
correlation disappears in both of the resulting subensembles if there is no
causal connection between these correlated events. These subensembles can be
regarded as common causes. Hofer-Szab\'{o} and R\'{e}dei (2004) generalized a
Reichenbachian common cause, and called it a Reichenbachian common cause
system. In the case of Reichenbachian common cause systems the statistical
ensemble is divided more than two, while it is divided into two parts in the
case of Reichenbachian common causes. The number of these subensembles is
called the size of this system. In the present paper, we examine Reichenbachian
common cause systems in general probability theories which include classical
probability theories and quantum probability theories. It is shown that there
is no Reichenbachian common cause system for any correlation between two events
which are not logical independent, and that a general probability theory which
is represented by an atomless orthomodular lattice with a faithful
$\sigma$-additive probability measure contains Reichenbachian common cause
systems of size 3 for any correlation between two compatible and logical
independent events. Moreover, we discuss a relation between Bell's inequality
and Reichenbachian common cause systems, and point out that this violation of
Bell's inequality can be compatible with a Reichenbachian common cause system
although it contradicts a `common' common cause system.
