In a dihybrid test cross, the proportion of individuals showing recessive phenotypes would be

Options

A. `1//16`
B. `7//16`
C. `1//4`
D. `3//4`

Answer

To solve the question about the proportion of individuals showing recessive phenotypes in a dihybrid test cross, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Test Cross**: A test cross is performed between an F1 hybrid (heterozygous for both traits) and a homozygous recessive individual. This helps to determine the genotype of the F1 individual.

2. **Identify the Traits**: Let's denote two traits with alleles A and B. The F1 individual will have the genotype AaBb (heterozygous for both traits), while the homozygous recessive individual will have the genotype aabb.

3. **Set Up the Cross**: The dihybrid test cross can be represented as:
- F1: AaBb
- Test Cross Parent: aabb

4. **Determine the Gametes**: The F1 individual (AaBb) can produce four types of gametes:
- AB
- Ab
- aB
- ab

5. **Perform the Punnett Square**: When we cross AaBb with aabb, we can create a Punnett square to visualize the offspring:
- The combinations will be:
- AB (from AaBb) x ab (from aabb) = AaBb
- Ab (from AaBb) x ab (from aabb) = Aabb
- aB (from AaBb) x ab (from aabb) = aaBb
- ab (from AaBb) x ab (from aabb) = aabb

6. **Count the Phenotypes**: The resulting phenotypes from the cross will be:
- 1 AaBb (dominant for both traits)
- 1 Aabb (dominant for A, recessive for B)
- 1 aaBb (recessive for A, dominant for B)
- 1 aabb (recessive for both traits)

7. **Calculate the Proportion of Recessive Phenotypes**: Out of the 4 offspring:
- 1 shows the recessive phenotype (aabb).
- Therefore, the proportion of individuals showing recessive phenotypes is 1 out of 4, which can be expressed as \( \frac{1}{4} \).

8. **Conclusion**: The proportion of individuals showing recessive phenotypes in a dihybrid test cross is \( \frac{1}{4} \).

### Final Answer:
The proportion of individuals showing recessive phenotypes in a dihybrid test cross is \( \frac{1}{4} \).

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