  We study online contention resolution schemes (OCRSs) and prophet
inequalities for non-product distributions. Specifically, when the active set
is sampled according to a pairwise-independent (PI) distribution, we show a
$(1-o_k(1))$-selectable OCRS for uniform matroids of rank $k$, and
$\Omega(1)$-selectable OCRSs for laminar, graphic, cographic, transversal, and
regular matroids. These imply prophet inequalities with the same ratios when
the set of values is drawn according to a PI distribution. Our results
complement recent work of Dughmi, Kalayci, and Patel (STOC '24) showing that no
$\omega(1/k)$-selectable OCRS exists in the PI setting for general matroids of
rank $k$.
