In humans, hair color is controlled by two interacting genes. The same?

In humans, hair color is controlled by two interacting genes. The same

pigment, melanin, is present in both brown-haired and blond-haired people, but brown

hair has much more of it. Brown hair (B) is dominant to blond (b). Whether any melanin

can be synthesized depends on another gene. The dominant form (M) allows melanin

synthesis; the recessive form (m) prevents melanin synthesis. Homozygous recessives

(mm) are albino. What will be the expected proportions of phenotypes in the children of

the following parents?

a.BBMM x BbMm

b.BbMm x bbmm

In humans, hair color is controlled by two interacting genes. The same?

Hair color is not as simple a matter as two genes interacting. There are other pigments, not just melanin. There are innumerable shades of hair color, like eye colors. How does this 2 gene thoery explain red hair? Sable? Black?

Assuming what you said, though, simple 4x4 punnet squares can solve this easily - assuming these genes assort indepentently. You probably have plenty of examples. What you have is a homozygous dominant bred to a true heterozygote in example A - this is like a F1xparent cross.

Example B gives a heterozygote with a homozygous recessive - also a type of F1xparent cross.

Case b is a simple 1:2:1 ratio - 1(Bbmm), 2(BbMm),1(bbmm) - half of these would in theory be albinos, half true hetrozygotes with medium brown hair.

Case a gives equal chances for 4 genotypes - BBMM, BBMm, BbMM, BbMm - all dark to medium brown haired.

But, as I said, this is an over-simplification. Where is blond defined? Are you assuming that the number of B copies gives darker shades? Dominant does not mean that. If B is dominant to b, then as long as a B is present, b will not show. If they both influence the physical expression of a gene, then B and b would be co-dominant. In this example there are 3 hair colors globally - brown, blonde and albino.