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A class of plausible inequalities between conditional probabilities is considered involving random subsets of a set which arise, for example, in studying the capacity of a multiple access channel. Some of the inequalities are true and can be proved by the Fortuin-Kasteleyn-Ginibre (FKG) inequality. Some others are true but seem to need other methods. Still others are false. The results also apply to studying the conditional probability of the failure of a device designed to achieve reliability by using redundant parts, given side information about the failure of some of its components.