Rule-based expert systems are those in which a certain number of IF-THEN rules are assumed to hold. Based on the verity of some assertions, the rules deduce new conclusions. In many cases, neither the rules nor the assertions are known with certainty. The system must then be able to obtain a measure of partial belief in the conclusion based upon measures of partial belief in the assertions and the rule. A problem arises when two or more rules (items of evidence) argue for the same conclusion. As proven in , certain assumptions concerning the independence of the two items of evidence is necessary before the certainties can be combined. In the current paper, it is shown how the well known MYCIN model combines the certainties from two items of evidence. The validity of the model is then proven based on the model's assumptions of independence of evidence. The assumptions are that the evidence must be independent in the whole space, in the space of the conclusion, and in the space of the complement of the conclusion. Next a probability-based model is described and compared to the MYCIN model. It is proven that the probabilistic assumptions for this model are weaker (independence is necessary only in the space of the conclusion and the space of the complement of conclusion), and therefore more appealing. An example is given to show how the added assumption in the MYCIN model is, in fact, the most restrictive assumption. It is also proven that, when two rules argue for the same conclusion, the combinatoric method in a MYCIN version of the probability-based model yields a higher combined certainty than that in the MYCIN model. It is finally concluded that the probability-based model, in light of the comparison, is the better choice.