What are the genotypes of all three horses

In horses, trotter (T) is dominant to pacer (t), and black coat color (B) is dominant to brown (b). A black horse who is a pacer mates with a brown horse who is a trotter. The resulting foal is a brown pacer. Give the genotypes of all three horses. Show work.

Black pacer parent:

Brown trotter parent:

Brown pacer foal:

Start with what you know. The foal is recessive for both genes, therefore can have only one genotype

bbtt, it is brown - homozygous recessive and a pacer homozygous recessive.

The black pacer parent is recessive for pacing tt. It passes on a b allele to its foal, but is black, so must have genotype Bb. Overall Bbtt.

The brown trotter is the reverse, bb for colour, but passes on a t allele to the foal despite being a trotter itself, therefore Tt. Overall bbTt.