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 with two alleles (dominant and recessive). This means we are dealing with four genes.

2. **Calculating Offspring Combinations**: For a tetrahybrid cross, the number of possible combinations of phenotypes can be calculated using the formula \(2^n\), where \(n\) is the number of traits. Here, \(n = 4\):
\[ 2^4 = 16 \]
This means there are 16 different combinations of alleles in the F1 generation.

3. **F2 Generation Offspring**: When we perform a cross of the F1 generation (which is heterozygous for all traits), the F2 generation will have a total of:
\[ 16 \times 16 = 256 \]
This indicates that there are 256 different phenotypic combinations in the F2 generation.

4. **Identifying Parental Phenotype Resemblance**: In a tetrahybrid cross, the offspring that resemble the phenotype of the parents will be those that have the same combination of dominant and recessive traits as the parents. Given the complexity of combinations, the likelihood of obtaining the same phenotype as the parents is quite low.

5. **Calculating the Proportion**: Out of the 256 possible offspring, only one combination will exactly match the parental phenotype. Therefore, the proportion of offspring that resemble the phenotype of the parents is:
\[ \frac{1}{256} \]

### Final Answer:
The proportion of offspring in the F2 generation of a tetrahybrid cross that will resemble the phenotype of the parents is \( \frac{1}{256} \).

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