Probabilities of Independent Choices Being Ordered

摘要

A simple proof of the following result of Baumert et al. is given. IfAandBare chosen independently according to a probability distribution defined on subsets of annelement set, then the probability thatAcontainsBis at least . It's shown to lead to a stronger conclusion, and to suggest definition of concepts of “partition number” and of “orthogonality of partitions into chains” as well as several conj