A mother with blood type 1Bi and a father with blood type 1A1B have children.?

The mother with blood 1Bi is carrying a B gene, and a nonfunctional gene.  The father with blood type 1A1B is carrying a B gene and an A gene.

Each parent gives 1 gene copy to their kids, so the possibilities are:

1B1A
1B1B
i1A
i1B

Type AB, B, A, and B are all possibilities.  O is not (O is ii).  D is the answer.

Hemophilia:

This is a gene carried on the X chromosome.  Men only have one copy of the X chromosome, so if they carry the gene, they have hemophilia.  This means that the woman's father does not have hemophilia.  The mother could not affect her son.

However, the mother could have picked up a hemophilia gene from her mother.  Women have 2 copies of the X chromosome, and hemophilia is a recessive.  That means that women can be carriers of the gene without having the disease.