Reichenbach's Common Cause Principle states that if there exists a probabilistic correlation between two events then either there is a direct causal connection between the correlated events or there exists a (Reichenbachian) common cause that explains the correlation. Assuming that the Common Cause Principle is valid, one is led to the question of whether theories that predict probabilistic correlations can be causally closed in the sense of containing also the causes of the correlations. The talk formulates this problem precisely and explicitly in terms of classical (Kolmogorovian) probability theory and presents results and open problems concerning causal closedness and common cause completeability of common cause incomplete probability spaces.