If you have a homozygous b blood female who mates with a heterozygous a blood male , what are the possible blood type of their children? ( human genes)

Homozygous B means that the female posses 
Heterozygous A means that the male posses  (A and B are both dominant while O is recessive to the two so if it is heterozygous A or B then O must be the other allele.

View the Punnett Cross below:

Thus based on the cross, there is a 50% chance that the offspring would be blood type AB and 50% chance the offspring would be blood type B.

Note: the blood type is the superscript on the base I.