To find the frequency of the [tex]\( p \)[/tex] (pink) allele in the plant population, we need to follow these steps:
1. Determine the total number of alleles in the population:
- Consider the number of alleles for each phenotype.
- The number of [tex]\( P \)[/tex] (purple) alleles is 150.
- The number of [tex]\( p \)[/tex] (pink) alleles is 20.
- The number of [tex]\( w \)[/tex] (white) alleles is 30.
Add these together to get the total number of alleles:
[tex]\[
\text{Total alleles} = 150 + 20 + 30 = 200
\][/tex]
2. Calculate the frequency of the [tex]\( p \)[/tex] allele:
- The frequency of a specific allele is the number of that particular allele divided by the total number of alleles in the population.
Hence, the frequency of the [tex]\( p \)[/tex] (pink) allele is:
[tex]\[
\text{Frequency of } p = \frac{\text{Number of } p \text{ alleles}}{\text{Total number of alleles}} = \frac{20}{200} = 0.10
\][/tex]
Given the calculations, the correct frequency of the [tex]\( p \)[/tex] allele is:
[tex]\[
\boxed{0.10}
\][/tex]
Thus, the correct answer is:
\textbf{B. 0.10}
