Final answer:
X-linked recessive inheritance is the most likely mode of inheritance for this rare, undiagnosed disease affecting the family.
Step-by-step explanation:
X-linked recessive inheritance is the most likely mode of inheritance for this rare, undiagnosed disease affecting the family. This is because affected males never produce affected children, but affected females do produce affected children of both sexes when they mate with unaffected males. With X-linked recessive diseases, males can either have the disease or be genotypically normal, while females can be carriers or affected. The disease affects more males than females, and examples of X-linked recessive diseases include color blindness, hemophilia, and some forms of muscular dystrophy.