Mating is an operation to construct a rational map from a pair of polynomials; since polynomials are classified by their Hubbard trees, this talk addresses the expected topology about mating random trees satisfying certain combinatorial conditions. Joint work with Insung Park provides a criterion to detect when a mating has a carpet when both polynomials are post-critically finite (PCF). Ongoing work in progress seeks to quantify the likelihood of an arbitrary quadratic PCF mating being a carpet based on the geography of the Mandelbrot set, and we discuss limitations of the approach. Finally we present related work towards a more general conjecture that generic d=2 hyperbolic rational maps have carpet Julia set, particularly addressing the case of the parameter space Per_n(0) with n prime.