A mother is fearful that the hospital sent her home with the wrong baby she has type B blood and her husband has type AB their baby is type O did the hispital make a mistake

Yes, there was a mistake

Explanation:

The mother is of type B blood whose genotype can be BB or BO

The father is of type AB blood whose genotype is AB

The baby is of type O blood whose genotype is OO

Thus, if the mother is of BB and the father AB, the can only produce children of AB and B bloodtype.

If the mother is of BO and the father AB, the can only produce children of AB, A and B bloodtype. There will not be able to produce a child of O bloodtype in an of the cases above.