Sure, let's solve this step by step.
We are given the genotypes of the parents:
- Parent 1: [tex]\(X^R X^r\)[/tex] (female, one normal vision allele [tex]\(X^R\)[/tex] and one color-deficient allele [tex]\(X^r\)[/tex])
- Parent 2: [tex]\(X^R Y\)[/tex] (male, normal vision allele [tex]\(X^R\)[/tex] and Y chromosome)
Since color-deficient vision is a sex-linked recessive trait, it is carried on the X chromosome. Only males with [tex]\(X^r Y\)[/tex] and females with [tex]\(X^r X^r\)[/tex] will express the trait.
1. Construct the Punnett Square:
Let's consider the alleles that each parent can pass on to their children.
For the mother ([tex]\(X^R X^r\)[/tex]):
- She can pass on [tex]\(X^R\)[/tex] or [tex]\(X^r\)[/tex].
For the father ([tex]\(X^R Y\)[/tex]):
- He can pass on [tex]\(X^R\)[/tex] or [tex]\(Y\)[/tex].
The possible combinations are as follows:
[tex]\[
\begin{array}{c|cc}
& X^R & Y \\
\hline
X^R & X^R X^R & X^R Y \\
X^r & X^R X^r & X^r Y \\
\end{array}
\][/tex]
2. Determine the Genotypic Outcomes:
There are four possible outcomes for the children's genotypes:
- [tex]\(X^R X^R\)[/tex] (female, healthy)
- [tex]\(X^R X^r\)[/tex] (female, carrier)
- [tex]\(X^R Y\)[/tex] (male, healthy)
- [tex]\(X^r Y\)[/tex] (male, color-deficient)
3. Calculate the Probabilities:
Next, we calculate the probability of each genotype by examining the Punnett Square:
- Probability of [tex]\(X^R X^R\)[/tex] (healthy female): 1 out of 4 chance [tex]\((1/4)\)[/tex]
- Probability of [tex]\(X^R X^r\)[/tex] (carrier female): 1 out of 4 chance [tex]\((1/4)\)[/tex]
- Probability of [tex]\(X^R Y\)[/tex] (healthy male): 1 out of 4 chance [tex]\((1/4)\)[/tex]
- Probability of [tex]\(X^r Y\)[/tex] (color-deficient male): 1 out of 4 chance [tex]\((1/4)\)[/tex]
4. Answer the Question:
The question wants to know the probability that the child will have color-deficient vision. Only the genotype [tex]\(X^r Y\)[/tex] results in color-deficient vision.
Therefore, the probability that the child will have color-deficient vision is [tex]\( \frac{1}{4} \)[/tex] or 0.25.
So, the correct answer is:
A. 0.25
