What is the fraction of individuals with double homozygous condition in a mendelian dihybrid across?

Options

A. 1/16
B. 2/16
C. 6/16
D. 9/16

Answer

To solve the question regarding the fraction of individuals with a double homozygous condition in a Mendelian dihybrid cross, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Double Homozygous Condition**:
- In genetics, a double homozygous condition refers to an individual that has two identical alleles for two different genes. For example, this can be represented as either:
- Homozygous dominant for both traits: \( YYRR \)
- Homozygous recessive for both traits: \( yyrr \)

2. **Identify the Traits in the Cross**:
- In this case, we are considering a dihybrid cross involving two traits, such as seed shape (round vs. wrinkled) and seed color (yellow vs. green).
- Let’s assume:
- Round seeds (R) are dominant over wrinkled seeds (r).
- Yellow seeds (Y) are dominant over green seeds (y).

3. **Set Up the Punnett Square**:
- For a dihybrid cross, we can set up a Punnett square that includes all combinations of alleles from both parents.
- Each parent can contribute one of two alleles for each trait, leading to a 4x4 Punnett square with 16 possible combinations.

4. **Count the Double Homozygous Combinations**:
- From the Punnett square, we can identify the combinations that represent the double homozygous conditions:
- \( YYRR \) (homozygous dominant for both traits)
- \( yyrr \) (homozygous recessive for both traits)
- There are 2 combinations that fit the double homozygous condition.

5. **Calculate the Fraction**:
- The total number of progeny (individuals) in the Punnett square is 16.
- The fraction of individuals with the double homozygous condition is calculated as:
\[ \text{Fraction} = \frac{\text{Number of double homozygous individuals}}{\text{Total number of individuals}} = \frac{2}{16} \]
- Simplifying this fraction gives:
\[ \frac{2}{16} = \frac{1}{8} \]

6. **Conclusion**:
- Therefore, the fraction of individuals with the double homozygous condition in a Mendelian dihybrid cross is \( \frac{1}{8} \).