It is given that the allele B for the black coat is dominant over allele b for a brown coat.
A dominant allele always leads to the expression of the dominant trait in the heterozygous condition.
When a black and brown horse is crossed as given in the question and the result is a brown foal, then the genotype of the brown foal must be bb as the brown coat is a recessive trait.
Since each parent contributes one allele each for a given gene, the black horse must have b allele, and hence must be heterozygous Bb.
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