What proportion of offsprings in the F.. generation of a tetrahybrid cross will resemble the phenotype of parents that produce the F.. hybrid ?

Options

A. 1/128
B. 1/256
C. 1/1024
D. `1//64`

Answer

To solve the question regarding the proportion of offspring in the F2 generation of a tetrahybrid cross that will resemble the phenotype of the parents producing the F1 hybrid, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Tetrahybrid Cross**:
A tetrahybrid cross involves four different traits, each represented by a different gene. In a tetrahybrid cross, we are considering the inheritance of four traits simultaneously.

2. **Determining the Number of Offspring**:
In a tetrahybrid cross, the F1 generation will be heterozygous for all four traits (e.g., AaBbCcDd). When these F1 individuals are crossed, the F2 generation will produce a large number of offspring. The total number of phenotypic combinations in the F2 generation can be calculated using the formula \(2^n\), where \(n\) is the number of traits. For four traits, \(n = 4\):
\[ 2^4 = 16 \text{ different phenotypes} \]

3. **Calculating the Total Offspring**:
When considering the F2 generation from a tetrahybrid cross, the total number of offspring produced is \(16^2 = 256\). This is because each trait can independently assort, leading to a total of 256 unique combinations of phenotypes.

4. **Identifying Parental Phenotype**:
In a tetrahybrid cross, the parental phenotype will only be represented once among the 256 combinations. Thus, the proportion of offspring that will resemble the phenotype of the parents is:
\[ \frac{1}{256} \]

5. **Conclusion**:
Therefore, the proportion of offspring in the F2 generation that will resemble the phenotype of the parents producing the F1 hybrid is \( \frac{1}{256} \) or approximately 0.39%.