* Long hair is dominant: Since half the offspring are long-haired, the long-haired parent must carry at least one dominant allele for long hair.
* Short hair is recessive: The other half of the offspring are short-haired, meaning they received a recessive allele for short hair from both parents. This indicates that the short-haired parent must carry two recessive alleles for short hair.
Therefore, we can conclude that the long-haired parent is heterozygous for hair length, meaning it has one dominant allele for long hair and one recessive allele for short hair.
Let's represent the alleles:
* L: Dominant allele for long hair
* l: Recessive allele for short hair
The possible genotypes and phenotypes of the offspring are:
* LL: Long hair (from long-haired parent and short-haired parent)
* Ll: Long hair (from long-haired parent and short-haired parent)
* ll: Short hair (from short-haired parent and short-haired parent)
This 1:1 ratio of long-haired to short-haired offspring is consistent with a heterozygous long-haired parent and a homozygous recessive short-haired parent.