To determine the frequency of the allele that codes for brown fur [tex]\((B_1)\)[/tex], follow these steps:
1. List All Alleles:
Extract all the alleles from the given table.
The table is:
```
W1 B2 B1
B1 W1 B2
B1 W1 B2
B2 B1 B2
W1 B2 W1
W1 B2 B1
```
Combine all the alleles into a single list:
```
W1, B2, B1, B1, W1, B2, B1, W1, B2, B2, B1, B2, W1, B2, W1, W1, B2, B1
```
2. Count the Total Number of Alleles:
Count the number of elements in the list. There are 18 alleles in total.
3. Count the Occurrences of the Brown Fur Allele [tex]\(B_1\)[/tex]:
Identify how many times [tex]\(B_1\)[/tex] appears in the list. The allele [tex]\(B_1\)[/tex] appears 5 times.
4. Calculate the Frequency of [tex]\(B_1\)[/tex]:
The frequency of an allele is given by the number of occurrences of that allele divided by the total number of alleles. So, the frequency of [tex]\(B_1\)[/tex] is:
[tex]\[
\text{Frequency of } B_1 = \frac{\text{Number of } B_1 \text{ alleles}}{\text{Total number of alleles}} = \frac{5}{18}
\][/tex]
5. Match to the Given Choices:
Compare the computed frequency with the provided options:
- [tex]\(A. \frac{13}{18}\)[/tex]
- [tex]\(B. \frac{5}{5}\)[/tex]
- [tex]\(C. \frac{5}{13}\)[/tex]
- [tex]\(D. \frac{5}{18}\)[/tex]
The correct choice is:
```
D. [tex]\(\frac{5}{18}\)[/tex]
```
Therefore, the frequency of the allele that codes for brown fur [tex]\((B_1)\)[/tex] in this population is [tex]\( \frac{5}{18} \)[/tex], which corresponds to option D.
