Pure homozygous offpriings in a silhbrid cross in the `F_(2) ` generation will be

Options

A. `1//2`
B. `1//4`
C. `1//8`
D. `1//16`

Explanation

To solve the question regarding the number of pure homozygous offspring in a dihybrid cross in the F2 generation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Dihybrid Cross**:
A dihybrid cross involves two traits, each represented by two alleles. For example, consider two traits: seed shape (round R and wrinkled r) and seed color (yellow Y and green y).

2. **Determine the Genotypes of Parents**:
Assume both parents are heterozygous for both traits (RrYy). The parental genotypes would be RrYy x RrYy.

3. **Create a Punnett Square**:
A dihybrid cross results in a 16-cell Punnett square. Each cell represents a possible genotype of the offspring. The combinations will include all possible combinations of the alleles from both parents.

4. **Count the Total Offspring**:
In the F2 generation, there will be 16 different combinations of alleles (genotypes) from the Punnett square.

5. **Identify Homozygous Offspring**:
Homozygous offspring are those with identical alleles for both traits. In our example, the homozygous combinations would be:
- RRYY (homozygous round yellow)
- RRYy (homozygous round yellow, but heterozygous for color)
- RrYY (heterozygous for shape, but homozygous yellow)
- rryy (homozygous wrinkled green)
- rryY (homozygous wrinkled green, but heterozygous for color)
- rrYY (homozygous for shape, but heterozygous for color)
- Rryy (heterozygous for shape, but homozygous green)
- RryY (heterozygous for both traits)
- RrYy (heterozygous for both traits)

The only pure homozygous combinations are RRYY and rryy. Thus, there are 2 homozygous combinations.

6. **Calculate the Ratio**:
Out of 16 total combinations, only 2 are pure homozygous. Therefore, the ratio of pure homozygous offspring is:
\[ \text{Ratio of homozygous} = \frac{2}{16} = \frac{1}{8} \]

7. **Conclusion**:
The answer to the question is that the proportion of pure homozygous offspring in the F2 generation of a dihybrid cross is \( \frac{1}{8} \).