What are the chances of our child ending up having depression or being bipolar, if there is no family history?

Same as general pop: Statistically 1% of population have bipolar and 6% major depression. Including all depressive symptoms the numbers seem greater. Without a family history, i generally look for more medical causes and stressors and would put more emphasis on psychotherapy in young person. In either case evaluation and treatment is in order to prevent deterioration in function.

Fortunately low: The chances are fortunately low. Most people who experience mood disorders have an inherited genetic propensity. However, it is still possible for a child to have depression or bipolar disorder even with no family history, as genetics are not the only factor. Social environment, stressful life events, and outlook can all impact the likelihood of mood disorders arising.