To determine the probability of an offspring being short and having white flowers, we need to focus on the specific genotype that corresponds to these traits.
1. Trait Analysis:
- The allele for tall plants ( [tex]\( T \)[/tex] ) is dominant over the allele for short plants ( [tex]\( t \)[/tex] ). Hence, for the plant to be short, its genotype must be [tex]\( tt \)[/tex].
- The allele for purple flowers ( [tex]\( P \)[/tex] ) is dominant over the allele for white flowers ( [tex]\( p \)[/tex] ). Hence, for the flowers to be white, the genotype must be [tex]\( pp \)[/tex].
Therefore, an offspring needs to have the genotype [tex]\( ttpp \)[/tex] to be short and have white flowers.
2. Identifying the Desired Genotype:
We need to look at the given Punnett square and count the occurrences of [tex]\( ttpp \)[/tex]:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\cline { 2 - 5 } & TP & Tp & tP & tp \\
\hline
TP & TTPP & TTPp & TtPP & TtPp \\
\hline
Tp & TTPp & TTpp & TtPp & Ttpp \\
\hline
tP & TtPP & TtPp & ttPP & ttPp \\
\hline
tp & TtPp & Ttpp & ttPp & ttpp \\
\hline
\end{array}
\][/tex]
Within the Punnett square, the total number of possible genotypes is [tex]\( 4 \times 4 = 16 \)[/tex].
Next, we need to find [tex]\( ttpp \)[/tex] in the Punnett square:
- The genotype [tex]\( ttpp \)[/tex] occurs only once (in the bottom right cell).
3. Calculating the Probability:
The total number of possible offspring from this Punnett square is [tex]\( 16 \)[/tex].
The number of occurrences of the [tex]\( ttpp \)[/tex] genotype is [tex]\( 1 \)[/tex].
Therefore, the probability of an offspring being short and having white flowers is:
[tex]\[
\text{Probability} = \frac{\text{Number of } ttpp \text{ occurrences}}{\text{Total number of possible offspring}} = \frac{1}{16}
\][/tex]
Given these steps and conclusions, the correct answer is:
D. [tex]\(\frac{1}{16}\)[/tex]
