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In pea plants, the allele for tall plants (T) is dominant over the allele for short plants (t). The allele for purple flowers (P) is dominant over the allele for white flowers (p). Two plants that are heterozygous for both traits are crossed, as shown in the 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]

What is the probability of an offspring being tall and having purple flowers?

A. 0.1875
B. 0.75
C. 0.5625
D. 0.0625

Sagot :

GinnyAnswer
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
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