How likely is it that a child will inherit adult diabetes and adult arthritis, if one parent has both problems?

Diabetes far more! Type-2 dm, secondary to metabolic sydrome, is much more herditable. If both parents have type 2 dm, an offspring is at least 80% likely to get diabetes. In contrast, only 30% of people with the most hereditable arthritis, ankylosing spondylitis will have sacroiliitis on x-ray, but most of them have only minor sx.