This talk features the passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeled as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural(non-technical) language.