To determine the probability of an offspring being tall and having purple flowers, let's follow these steps:
1. Identify the Relevant Genotypes:
- Tall plants have at least one [tex]\(T\)[/tex] allele (either [tex]\(TT\)[/tex] or [tex]\(Tt\)[/tex]).
- Plants with purple flowers have at least one [tex]\(P\)[/tex] allele (either [tex]\(PP\)[/tex] or [tex]\(Pp\)[/tex]).
2. Examine the Genotypes in the Punnett Square:
We need to count the number of squares in the Punnett square that have at least one [tex]\(T\)[/tex] and one [tex]\(P\)[/tex].
Here are the genotypes from the given Punnett square:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline & TP & Tp & tP & tp \\
\hline TP & TTPP & TTPp & TtPP & TtPp \\
\hline Tp & TTPp & TTpp & TtPp & Ttpp \\
\hline tP & TtPP & TtPp & ttPP & ttPp \\
\hline tp & TtPp & Ttpp & ttPp & ttpp \\
\hline
\end{array}
\][/tex]
3. Count the Genotypes that are Tall and Purple:
We need the genotypes that contain both [tex]\( T \)[/tex] and [tex]\( P \)[/tex]. These are:
- [tex]\(TTPP\)[/tex]
- [tex]\(TTPp\)[/tex]
- [tex]\(TtPP\)[/tex]
- [tex]\(TtPp\)[/tex]
Going through the squares one by one:
- [tex]\(TTPP\)[/tex]
- [tex]\(TTPp\)[/tex]
- [tex]\(TtPP\)[/tex]
- [tex]\(TtPp\)[/tex]
- [tex]\(TTPp\)[/tex]
- [tex]\(TtPp\)[/tex]
- [tex]\(TtPP\)[/tex]
- [tex]\(TtPp\)[/tex]
- [tex]\(TtPp\)[/tex]
There are 9 such genotypes.
4. Calculate the Probability:
There are 16 total possible outcomes in the Punnett square as it is a 4x4 grid.
Therefore, the probability is the number of favorable outcomes divided by the total number of possible outcomes:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{9}{16}
\][/tex]
Converting [tex]\(\frac{9}{16}\)[/tex] to a decimal, we get:
[tex]\[
\frac{9}{16} = 0.5625
\][/tex]
Hence, the probability of an offspring being tall and having purple flowers is [tex]\(0.5625\)[/tex], which corresponds to option C.
Final Answer: C. 0.5625
