2 problems

Let $K$ be an $n$-dimensional convex body. A weighted collection of light sources illuminates $K$ if every boundary point is illuminated by sources whose total weight is at least…

Let $X$ be a finite set and let ${\mathcal F}\subseteq2^X$ be increasing. Let $q({\mathcal F})$ be the expectation-threshold and $q_f({\mathcal F})$ the fractional expectation-thre…