If a mother has brown eyes and a father has blue eyes why do two of their children have blue eyes and one have brown eyes?

The eye color of an individual is determined by the combination of genes they inherit from their parents. Different variations of a gene, called alleles, determine the color of the eyes. The two main eye color alleles are for brown (dominant allele) and blue (recessive allele) eyes.

In this case, the mother has brown eyes, which indicates that she carries at least one brown eye allele. The father has blue eyes, so he carries two blue eye alleles. When they have children, each parent randomly passes on one allele for each of their genes to their offspring.

To determine the possible combinations, let's assume that the father's genotype is "bb" (two copies of the blue allele) and the mother's genotype is "Bb" (one copy of the brown allele and one copy of the blue allele).

The combinations of alleles that the parents can pass on to their children are as follows:

- From the father: Each child has a 50% chance of inheriting a "b" allele (blue eye allele).
- From the mother: Each child has a 50% chance of inheriting a "B" allele (brown eye allele) and a 50% chance of inheriting a "b" allele.

Using Punnett square analysis or probability calculations, we can determine the potential outcomes:

- Child 1: Blue eye allele (b) from the father + Brown eye allele (B) from the mother = Brown eyes (Bb).
- Child 2: Blue eye allele (b) from the father + Blue eye allele (b) from the mother = Blue eyes (bb).
- Child 3: Blue eye allele (b) from the father + Blue eye allele (b) from the mother = Blue eyes (bb).

Therefore, two children have blue eyes (bb genotype) because they received a blue eye allele from both parents. The other child has brown eyes (Bb genotype) because they inherited a brown eye allele from the mother and a blue eye allele from the father.

In summary, the variation in eye color among the children is due to the random combination of alleles inherited from their parents.