The objective of the present article is twofold: first, to provide ways for eliciting consistent a priori and conditional probabilities for a set of events representing pieces of evidence and hypotheses in the context of a rule based expert system. Then an algorithm is proposed which uses the least possible number of a priori and conditional probabilities as its input and which computes the lower and upper bounds for higher order conditional and joint probabilities, so that these be consistent with the input probabilities provided. In the case, when inconsistent lower and upper bounds are obtained, it is suggested how the latter can be turned into consistent ones, by changing the values of only these input probabilities which are directly represented in the higher order probability under consideration. Secondly, a number of typical cases with respect to the problems of aggregation and propagation of uncertainty in expert systems is considered. It is shown how these can be treated by using higher order joint probabilities. For this purpose no global assumptions for independence of evidence and for mutual exclusiveness of hypotheses are required, since the presence of independent andlor dependent pieces of evidence, as well as the presence of mutually exclusive hypotheses, is explicitly encoded in the input probabilities and thus, such a presence is automatically detected by the algorithm when computing higher order joint probabilities.