The confinement of quarks is one of the enduring mysteries of modern physics. I will present a rigorous result that shows that if a pure lattice gauge theory at some given coupling strength has exponential decay of correlations under arbitrary boundary conditions, and the gauge group is a compact connected matrix Lie group with a nontrivial center, then the theory is confining. This gives mathematical justification for a longstanding belief in physics about the mechanism behind confinement, which roughly says that confinement is the result of strong coupling behavior plus center symmetry. The proof is almost entirely based in probability theory, making extensive use of the idea of coupling probability measures.