If the father has blood type O and the mother has blood type B, the child may have blood type O or B, but not blood type A or AB.
There are two antigenic sites on the surface of normal red blood cells, which originate from the father and the mother respectively. type O red blood cells do not have either type A or type B antigen on the surface of the blood group antigen, which can be expressed as ii; type B blood cells may have Bi or BB on the surface of the two antigenic sites.
If the father is type O and the mother is type B with BB, the child will be of blood type B. If the father is type O and the mother is type B with Bi, the child will be of blood type B or type O. In summary, a father with blood type O and a mother with blood type B may have a child with blood type O or blood type B. Since there is no A blood antigen, there can be no A or AB blood.