To determine the probability of an offspring being tall and having purple flowers, we need to analyze the content of the given Punnett square. The Punnett square for two traits (plant height and flower color) when both parents are heterozygous (TtPp) will have 16 possible outcomes.
Let's list all the possible combinations in the Punnett square and identify those corresponding to tall plants (at least one 'T') and purple flowers (at least one 'P'):
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline & T P & T p & t P & t p \\
\hline T P & TT PP & TT Pp & Tt PP & Tt Pp \\
\hline T p & TT Pp & TT pp & Tt Pp & Tt pp \\
\hline t P & Tt PP & Tt Pp & tt PP & tt Pp \\
\hline t p & Tt Pp & Tt pp & tt Pp & tt pp \\
\hline
\end{array}
\][/tex]
Next, we need to count the number of outcomes where the offspring is tall and has purple flowers. An offspring will be tall if it has at least one 'T' allele. Similarly, it will have purple flowers if it has at least one 'P' allele.
Here's the breakdown of which combinations satisfy both conditions (tall i.e., containing 'T' and purple i.e., containing 'P'):
1. TT PP
2. TT Pp
3. Tt PP
4. Tt Pp
5. TT Pp
6. Tt Pp
7. Tt PP
8. Tt Pp
9. Tt Pp
By counting these combinations, we see that there are 9 favorable outcomes where the offspring is both tall and has purple flowers.
Since there are a total of 16 possible outcomes in the Punnett square, the probability of an offspring being tall and having purple flowers is:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{9}{16} = 0.5625
\][/tex]
Therefore, the probability of an offspring being tall and having purple flowers is:
C. 0.5625
