To determine the probability of an offspring being short with white flowers when two heterozygous pea plants (TtPp) are crossed, we need to examine the Punnett square provided.
Here's the Punnett square directly from the cross of TtPp x TtPp:
[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]
Let's analyze each Lattice of the Punnett square to find those that result in short plants with white flowers (ttpp):
- TTPP (Tall, Purple)
- TTPp (Tall, Purple)
- TtPP (Tall, Purple)
- TtPp (Tall, Purple)
- TTPp (Tall, Purple)
- TTpp (Tall, White)
- TtPp (Tall, Purple)
- Ttpp (Tall, White)
- TtPP (Tall, Purple)
- TtPp (Tall, Purple)
- ttPP (Short, Purple)
- ttPp (Short, Purple)
- TtPp (Tall, Purple)
- Ttpp (Tall, White)
- ttPp (Short, Purple)
- ttpp (Short, White)
From the analysis, only the combination ttpp results in short plants with white flowers. There is only 1 cell (ttpp) fitting this description.
Next, determine the total possible genotypes in the Punnett square, which is the sum total of all possible cells: [tex]\(16\)[/tex] cells.
To find the probability of getting an offspring genotype that is short and has white flowers, divide the number of favorable outcomes by the total possible outcomes:
[tex]\[
\text{Probability} = \frac{1 \text{ (ttpp) favorable outcome}}{16 \text{ (total possible outcomes)}} = \frac{1}{16}
\][/tex]
Therefore, the probability of an offspring being short and having white flowers is:
\[
\boxed{\frac{1}{16}}
\
