According the Hardy-Weinberg Principle, the allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.

 

For a single locus with two alleles, A and a, with their respective frequencies f(A) = p and f(a) = q, the expected genotype frequencies under random mating will be f(AA) = p² for the AA homozygotes, f(aa) = q² for the aa homozygotes, and f(Aa) = 2pq for the heterozygotes. In the absence of selection, mutation, etc., allele frequencies p and q are constant between generations, so equilibrium is reached.

 

Let the dominant trait be p and the recessive trait be q. 9% of the individuals are red-haired. So, according to Hardy-Weinberg Principle,

The frequency of heterozygotes is denoted by 2pq.

Hence,