Certainly! Let's go through the steps to find the frequency of the type B allele in the population.
### Step 1: Gather Information
We are given the following information:
- Number of individuals who are homozygous dominant type A (AA): 7
- Number of individuals who are heterozygous dominant type AB: 35
- Number of individuals who are homozygous dominant type B (BB): 8
### Step 2: Total Population
The total population can be calculated by summing the number of individuals in each genotype category:
[tex]\[ \text{Total Population} = \text{Number of AA} + \text{Number of AB} + \text{Number of BB} \][/tex]
[tex]\[ \text{Total Population} = 7 + 35 + 8 = 50 \][/tex]
### Step 3: Calculate the Total Number of B Alleles
To find the total number of B alleles in the population, count contributions from:
- Homozygous dominant type B (BB): Each individual contributes 2 B alleles.
- Heterozygous dominant type AB: Each individual contributes 1 B allele.
So, the total number of B alleles is computed as:
[tex]\[ \text{Total B Alleles} = (2 \times \text{Number of BB}) + \text{Number of AB} \][/tex]
[tex]\[ \text{Total B Alleles} = (2 \times 8) + 35 = 16 + 35 = 51 \][/tex]
### Step 4: Calculate the Frequency of the B Allele
The frequency of an allele in a population is given by:
[tex]\[ \text{Frequency of Allele B} = \frac{\text{Total B Alleles}}{\text{Total Number of Alleles}} \][/tex]
In a diploid population, each individual has 2 alleles, so the total number of alleles in the population is:
[tex]\[ \text{Total Number of Alleles} = 2 \times \text{Total Population} \][/tex]
[tex]\[ \text{Total Number of Alleles} = 2 \times 50 = 100 \][/tex]
Thus, the frequency of the B allele is:
[tex]\[ \text{Frequency of Allele B} = \frac{51}{100} = 0.51 \][/tex]
### Conclusion:
The frequency of the type B allele in this population is [tex]\( \boxed{0.51} \)[/tex].
