A woman with blood group O should have genotype i i i.e. Both of her parents should at least have one i allele. So for having a child with blood group B, there should be at least one parent having a copy of IB allele. Parents with Iai and Ibi will have children with Iai (A blood group), Ibi (B blood group), IaIb (AB blood group) and ii (O blood group).