What percentage of offsprings would have the genotype AA Bb Cc in `F_(2)` generation of a trihybrid cross -

Options

A. 0.125
B. 0.0625
C. 0.25
D. 0.375

Answer

To determine the percentage of offspring with the genotype AA Bb Cc in the F2 generation of a trihybrid cross, we can follow these steps:

### Step 1: Understand the Genotypes
In a trihybrid cross involving three traits (A, B, and C), we need to analyze the inheritance of each trait separately. The genotype AA indicates homozygous dominant for A, Bb indicates heterozygous for B, and Cc indicates heterozygous for C.

### Step 2: Determine the F2 Generation Ratios for Each Trait
For each trait, we can use the following ratios from a monohybrid cross:
- **For A (AA)**: The ratio of AA in F2 generation is 1/4 (from the cross AA x Aa).
- **For B (Bb)**: The ratio of Bb in F2 generation is 1/2 (from the cross Bb x Bb).
- **For C (Cc)**: The ratio of Cc in F2 generation is also 1/2 (from the cross Cc x Cc).

### Step 3: Calculate the Combined Probability
To find the combined probability of obtaining the genotype AA Bb Cc, we multiply the probabilities of each genotype:
- Probability of AA = 1/4
- Probability of Bb = 1/2
- Probability of Cc = 1/2

Now, we multiply these probabilities together:
\[ \text{Probability of AA Bb Cc} = \left(\frac{1}{4}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \]

### Step 4: Perform the Calculation
Calculating the above expression:
\[ \text{Probability of AA Bb Cc} = \frac{1}{4} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{16} \]

### Step 5: Convert to Percentage
To convert the probability into a percentage, we multiply by 100:
\[ \text{Percentage} = \frac{1}{16} \times 100 = 6.25\% \]

### Final Answer
Thus, the percentage of offspring with the genotype AA Bb Cc in the F2 generation of a trihybrid cross is **6.25%**.

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