Ben has red hair, and his wife has brown hair. The allele for red hair is recessive (r) and the allele for brown hair is dominant (B). Their son also has red hair. What is the genotype of Ben's wife?

We know red hair is recessive, so to have red hair you must have to have two red hair alleles, therefore Ben's genotype must be rr.However, the brown hair allele is dominant, this means you can have either one red and one brown hair allele ( Br) or two brown hair alleles (BB) and still have brown hair.So how do we know which genotype Ben's wife has?
Well the son also has red hair so must have the rr genotype, and we know that you inherit one allele from each parent. We know he must inherit one r allele from his father (rr), so in order to inherit an r from his mother, she must have the Br genotype not the BB genotype. If the mother had the BB genotype she would only be able to pass on a B allele and therefore all of the children would have brown hair.