If parents are A and B, what are the possible genotypes of the parents? What are all the possible blood types of children? What if the parents are AB and A?
With analyses of this type, we say that one gene comes from Dad and one from Mom, resulting in 2 genes within a child. Some genes are dominant (meaning that if they are present, they determine that particular factor) and others are recessive (so the 2 genes in a person must be the same for that quality to win out).
Quick example - Brown eyes are dominant and blue eyes are recessive. There are 3 different ways the two genes can be: BB, Bb, bb. The first 2 have the dominant Brown gene and so that person will have Brown eyes. The last one has both genes as b and so that person will have blue eyes.
Ok - on to the question!
There are 4 blood types:
O, A, B, AB
A and B are dominant genes. O is recessive. A and B are equally dominant so that when they get together they create a new blood type: AB.
A person with blood type A can have genotype: AA, AO
A person with blood type B can have genotype: BB, BO
A person with blood type O can have genotype OO
A person with blood type AB can have genotype AB
So what happens to a child of parents with blood types AB and A? We know that the AB parent will contribute either an A gene or a B gene to the child. The A parent may have a genome of AA or AO, so potentially can contribute an A gene or an O gene. Since there is more potential variety in a child with a parent with AO, let's assume the parent is that genome. So the child can have the following genotypes (I'll use subscripts to indicate where the genes are coming from):