Diagnosing an inherited disease often requires identifying the pattern of inheritance in a patient's family. We represent family trees with genetic patterns of inheritance using hypergraphs and latent state space models to provide explainable inheritance pattern predictions. Our approach allows for exact causal inference over a patient's possible genotypes given their relatives' phenotypes. By design, inference can be examined at a low level to provide explainable predictions. Furthermore, we make use of human intuition by providing a method to assign hypothetical evidence to any inherited gene alleles. Our analysis supports the application of latent state space models to improve patient care in cases of rare inherited diseases where access to genetic specialists is limited.