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Sagot :
To determine the percentage of offspring with the genotype represented by the letter [tex]\(A\)[/tex] in a Punnett square for a heterozygous cross (denoted as [tex]\(X x\)[/tex]), we need to carefully analyze the potential genotypes that can result from this cross.
1. Setup the Punnett Square:
In a heterozygous cross [tex]\(X x\)[/tex], both parents contribute one of two possible alleles (either [tex]\(X\)[/tex] or [tex]\(x\)[/tex]). We create a Punnett square to map out all possible combinations of these alleles.
2. Fill Out the Punnett Square:
Here's how the Punnett square looks for [tex]\(X x\)[/tex] (heterozygous cross):
| | X | x |
|----|-----|-----|
| X | XX | Xx |
| x | Xx | xx |
3. Identify the Possible Genotypes:
From the Punnett square, we can see the four possible combinations of alleles:
- [tex]\(XX\)[/tex]
- [tex]\(Xx\)[/tex]
- [tex]\(Xx\)[/tex]
- [tex]\(xx\)[/tex]
4. Count Each Genotype:
Let's count how many times each genotype appears:
- [tex]\(XX\)[/tex] appears 1 time.
- [tex]\(Xx\)[/tex] appears 2 times.
- [tex]\(xx\)[/tex] appears 1 time.
5. Calculate the Probability of Each Genotype:
Because each spot in the Punnett square represents an equally likely outcome, each genotype's probability can be represented as fractions of the total number of combinations (which is 4 in this case).
- Probability of [tex]\(XX\)[/tex] = [tex]\(\frac{1}{4}\)[/tex] = 25%
- Probability of [tex]\(Xx\)[/tex] = [tex]\(\frac{2}{4}\)[/tex] = 50%
- Probability of [tex]\(xx\)[/tex] = [tex]\(\frac{1}{4}\)[/tex] = 25%
6. Determine the Genotypes Represented by the Letter [tex]\(A\)[/tex]:
Without loss of generality, let's assume the letter [tex]\(A\)[/tex] represents all genotypes containing at least one [tex]\(X\)[/tex] allele, so genotypes [tex]\(XX\)[/tex] and [tex]\(Xx\)[/tex] will be grouped under [tex]\(A\)[/tex].
- Genotype [tex]\(XX\)[/tex] appears 1 out of 4 times.
- Genotype [tex]\(Xx\)[/tex] appears 2 out of 4 times.
Combining these probabilities: [tex]\(1/4\)[/tex] (for [tex]\(XX\)[/tex]) + [tex]\(2/4\)[/tex] (for [tex]\(Xx\)[/tex]) totals up to [tex]\(\frac{3}{4}\)[/tex].
7. Convert Fraction to Percentage:
- [tex]\(\frac{3}{4}\)[/tex] is equivalent to 75%.
Therefore, the percentage of offspring that will most likely have the genotype represented by the letter [tex]\(A\)[/tex] is 75%. So, the answer to the question is:
75%
1. Setup the Punnett Square:
In a heterozygous cross [tex]\(X x\)[/tex], both parents contribute one of two possible alleles (either [tex]\(X\)[/tex] or [tex]\(x\)[/tex]). We create a Punnett square to map out all possible combinations of these alleles.
2. Fill Out the Punnett Square:
Here's how the Punnett square looks for [tex]\(X x\)[/tex] (heterozygous cross):
| | X | x |
|----|-----|-----|
| X | XX | Xx |
| x | Xx | xx |
3. Identify the Possible Genotypes:
From the Punnett square, we can see the four possible combinations of alleles:
- [tex]\(XX\)[/tex]
- [tex]\(Xx\)[/tex]
- [tex]\(Xx\)[/tex]
- [tex]\(xx\)[/tex]
4. Count Each Genotype:
Let's count how many times each genotype appears:
- [tex]\(XX\)[/tex] appears 1 time.
- [tex]\(Xx\)[/tex] appears 2 times.
- [tex]\(xx\)[/tex] appears 1 time.
5. Calculate the Probability of Each Genotype:
Because each spot in the Punnett square represents an equally likely outcome, each genotype's probability can be represented as fractions of the total number of combinations (which is 4 in this case).
- Probability of [tex]\(XX\)[/tex] = [tex]\(\frac{1}{4}\)[/tex] = 25%
- Probability of [tex]\(Xx\)[/tex] = [tex]\(\frac{2}{4}\)[/tex] = 50%
- Probability of [tex]\(xx\)[/tex] = [tex]\(\frac{1}{4}\)[/tex] = 25%
6. Determine the Genotypes Represented by the Letter [tex]\(A\)[/tex]:
Without loss of generality, let's assume the letter [tex]\(A\)[/tex] represents all genotypes containing at least one [tex]\(X\)[/tex] allele, so genotypes [tex]\(XX\)[/tex] and [tex]\(Xx\)[/tex] will be grouped under [tex]\(A\)[/tex].
- Genotype [tex]\(XX\)[/tex] appears 1 out of 4 times.
- Genotype [tex]\(Xx\)[/tex] appears 2 out of 4 times.
Combining these probabilities: [tex]\(1/4\)[/tex] (for [tex]\(XX\)[/tex]) + [tex]\(2/4\)[/tex] (for [tex]\(Xx\)[/tex]) totals up to [tex]\(\frac{3}{4}\)[/tex].
7. Convert Fraction to Percentage:
- [tex]\(\frac{3}{4}\)[/tex] is equivalent to 75%.
Therefore, the percentage of offspring that will most likely have the genotype represented by the letter [tex]\(A\)[/tex] is 75%. So, the answer to the question is:
75%
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