Final answer:
The frequency of the recessive allele b in a population with 30 BB, 60 Bb, and 10 bb individuals is 40%. This is calculated by counting the total number of b alleles and dividing by the total number of alleles in the population.
Step-by-step explanation:
The frequency of the recessive allele b in a population can be calculated using the genotype frequencies. For a gene with two alleles, B and b, in a population of 100 individuals with the genotypes; 30 BB, 60 Bb, and 10 bb, we first need to find the total number of alleles for the gene which is twice the number of individuals since each individual carries two alleles. Next, we count the number of b alleles which is twice the number of bb individuals plus the number of Bb individuals since they have one allele of each type. To find the frequency of allele b, we divide the total number of b alleles by the total number of alleles in the population.
In this case, there are 10 bb individuals which contribute 20 b alleles and 60 Bb individuals each contributing 1 allele, so there are 60 more b alleles. Therefore, the total is 20 + 60 = 80 b alleles. The total number of alleles in the population is 100 individuals × 2 alleles per individual = 200 alleles. Thus, the frequency of the b allele is 80 divided by 200, which simplifies to 0.4 or 40%.