We know that the parents express as brown haired which means that they may have the genotypes BB and Bb. We know that for the children to express as red-haired, they must have two recessive genes. Because they get one gene from each parent, both parents must have one recessive gene.
B b B BB Bb b Bb bb
A couple with brown hair can have red-haired children if both parents carry the recessive allele for red hair. Using a Punnett square, we determine that the probability of having red-haired children is 25%. This aligns with the observed outcome of having three red-haired and two brown-haired children.
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