What is the possibility that a child will be a manic-depressive if her mother has that disorder?

Only somewhat higher: Although manic-depressive illness, or bipolar affective disorder) clearly has a strong genetic component, it also has what is called "low penetrance, " meaning that even if one or both of your parents have the disorder, your chances of not having it remain pretty good. With one parent have the disorder, the risk probably is 10-15%--much higher than the general risk but still not bad odds.

It varies: Many things may influence this and there may be different forms of bipolar that have different levels of heritability. For some families, it can be as high as 50%.

As Doctors : Moranville and Elliot stated this is not necessarily a straight forward issue- See: https://www.clinicalkey.com/topics/psychiatry/bipolar-disorder.html