The design and selection of pedagogically effective problem situations is a critical yet undertheorized facet of reform-oriented mathematics education. Drawing on instructional-design frameworks and cognitive-science theory, we propose a situation taxonomy centered on the dimensions “familiar” and “generic” and hypothesize the contrasting learning affordances of exponents thereof. 51 undergraduate students solved either a familiar or a generic version of a compound-probability problem, and subgroups thereof then participated in semi-structured clinical interviews. Familiar problems evoked common sense, yet their treatment was liable to be mathematically non-normative; generic problems triggered mathematically suitable treatments, yet these treatments were liable to remain opaque. We discuss implications of these tradeoffs with an eye to fostering mathematical-probabilistic literacy that is both powerful and grounded.