If my wife is hyperactive all of the time, what are the chances our child will also be just as hyperactive?

Hyperactivity: Hard to tell. It would be important to determine if there is another issue underlying or if it is a personality trait. If you are concerned consult with physician/specialist. Hyperactivity in kids can be sign of sleep disorder or inadequate sleep vs adults that get "tired' and "depressed.".

It depends: Hyperactivity is a symptom, like fever is a symptom. Different conditions contain hyperactivity as a part of an overall disorder. Usually, the hyperactivity as seen in attention deficit hyperactivity disorder or adhd, is a prominent symptom in kids, but not adults. Other conditions, like bipolar disorder may be associated with hyperactivity. Both bipolar disorder and adhd tend to run in families.