Noticing that the contribution variable has the same possible values as e, we define functions by
for any value of e. We shall refer to as the contributing factor of to e.
By using the operator , we can now rewrite equation (2) as follows
It is interesting to notice the similarity between equation (1) and equation (5). In equation (1) conditional independence allows one to factorize a joint probability into factors that involve less variables, while in equation (5) causal independence allows one to factorize a conditional probability into factors that involve less variables. However, the ways by which the factors are combined are different in the two equations.