A trihybrid plant was selfed and 2560 seeds were obtained. How many seeds will produce plant with all recessive characters ?

Options

A. 100
B. 40
C. 128
D. 256

Answer

To solve the problem of how many seeds will produce plants with all recessive characters from a trihybrid plant selfed to produce 2560 seeds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Genotype of the Trihybrid Plant**:
- A trihybrid plant has three traits, each represented by a pair of alleles. We can denote these alleles as A, a for the first trait; B, b for the second trait; and C, c for the third trait.
- Therefore, the genotype of the trihybrid plant can be represented as AaBbCc.

2. **Determine the Probability of All Recessive Traits**:
- For each trait, we want to find the probability of obtaining the homozygous recessive genotype (aa, bb, cc).
- The probability of getting the homozygous recessive genotype for each trait when crossing Aa x Aa, Bb x Bb, and Cc x Cc is as follows:
- For trait A (Aa x Aa):
- Possible genotypes: AA, Aa, Aa, aa → Probability of aa = 1/4
- For trait B (Bb x Bb):
- Possible genotypes: BB, Bb, Bb, bb → Probability of bb = 1/4
- For trait C (Cc x Cc):
- Possible genotypes: CC, Cc, Cc, cc → Probability of cc = 1/4

3. **Calculate the Combined Probability**:
- Since the traits are independent, we can multiply the probabilities of obtaining the recessive genotype for each trait:
\[ P(aa, bb, cc) = P(aa) \times P(bb) \times P(cc) = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64} \]

4. **Calculate the Expected Number of Seeds with All Recessive Characters**:
- Now, we need to find out how many of the 2560 seeds will produce plants with all recessive characters:
\[ \text{Number of seeds with all recessive characters} = P(aa, bb, cc) \times \text{Total seeds} = \frac{1}{64} \times 2560 \]
- Performing the calculation:
\[ \frac{2560}{64} = 40 \]

5. **Conclusion**:
- Therefore, the number of seeds that will produce plants with all recessive characters is **40**.