We consider a probabilistic antimatroid A on the ground set E, where each element e ∈ E may succeed with probability pe. We focus on the expected rank ER(A) of a subset of E as a polynomial in the pe. General formulas hold for arbitrary antimatroids, and simpler expressions are valid for certain well-studied classes, including trees, rooted trees, posets, and finite subsets of the plane. We connect the Tutte polynomial of an antimatroid to ER(A). When S is a finite subset of the plane with no… CONTINUE READING