Let's break down the question step-by-step:
1. Initial Cross (PP x pp):
- The genotype PP represents a pea plant with purple flowers.
- The genotype pp represents a pea plant with white flowers.
- When these two plants are crossed, all offspring will inherit one allele from each parent. Since P is dominant over p, all offspring will have the genotype Pp.
- Pp results in purple flowers because the dominant allele P masks the presence of the recessive allele p.
Therefore, the possibility that the offspring will have purple flowers is [tex]\(100\%\)[/tex] or [tex]\(1.0\)[/tex].
2. Second Cross (Pp x pp):
- Now, let’s consider the mating of an offspring from the first cross (Pp) with a plant having the genotype pp.
- We can use a Punnett Square to determine the possible genotypes of the next generation.
[tex]\[
\begin{tabular}{|c|c|c|}
\hline & P & p \\
\hline p & Pp & pp \\
\hline p & Pp & pp \\
\hline
\end{tabular}
\][/tex]
Here, the Punnett Square shows the following combinations:
- [tex]\(Pp\)[/tex] (Purple, because P is dominant)
- [tex]\(pp\)[/tex] (White, because both alleles are recessive)
- There are 4 possible outcomes:
- 2 of them are Pp (purple)
- 2 of them are pp (white)
- Therefore, the probability for each genotype is:
- [tex]\(Pp: \frac{2}{4} = 0.5\)[/tex]
- [tex]\(pp: \frac{2}{4} = 0.5\)[/tex]
- The question asks for the possibility of homozygous dominant genotype (PP), which isn’t possible in this scenario as there’s no P allele from pp parent to create a PP combination.
Therefore, the possibility of having the homozygous dominant genotype (PP) is [tex]\(0.0\)[/tex].
To summarize:
- The possibility that the offspring from the initial cross will have purple flowers is [tex]\(1.0\)[/tex].
- The possibility of the offspring from the second cross (Pp x pp) having the homozygous dominant genotype (PP) is [tex]\(0.0\)[/tex].
