A pure pea plant having yellow and round seeds in an inflated pod was crossed with a pure pea plant having green and wrinkled seeds in a constricted pod . The proportion of plants having green round seeds in an inflated pod in the `F_2` generation is

Options

A. `27/64`
B. `9/64`
C. `3/64`
D. `1/64`

Answer

To solve the problem, we need to analyze the genetic traits of the pea plants involved in the cross and determine the proportions of the resulting phenotypes in the F2 generation.

### Step-by-Step Solution:

1. **Identify the Traits and Their Alleles:**
- The first parent plant has:
- Yellow seeds (dominant, denoted as Y)
- Round seeds (dominant, denoted as R)
- Inflated pods (dominant, denoted as I)
- The second parent plant has:
- Green seeds (recessive, denoted as y)
- Wrinkled seeds (recessive, denoted as r)
- Constricted pods (recessive, denoted as i)

2. **Determine the Genotypes of the Parents:**
- The genotype of the first parent (homozygous dominant) is: YYRRII
- The genotype of the second parent (homozygous recessive) is: yyrrii

3. **Cross the Parents to Form the F1 Generation:**
- When these two plants are crossed, all offspring in the F1 generation will be heterozygous for all traits:
- F1 genotype: YyRrIi (Yellow, Round, Inflated)

4. **Cross the F1 Generation to Form the F2 Generation:**
- To find the F2 generation, we need to perform a dihybrid cross of the F1 generation (YyRrIi x YyRrIi).
- Since we are interested in three traits, we can use a Punnett square or apply the multiplication method for three traits.

5. **Calculate the Phenotypic Ratios in the F2 Generation:**
- According to Mendel's laws, for a tri-hybrid cross, the phenotypic ratio is 27:9:9:9:3:3:3:1.
- We are specifically looking for the phenotype of green round seeds in an inflated pod. This phenotype corresponds to:
- Green seeds (yy) - recessive
- Round seeds (R_) - dominant
- Inflated pod (I_) - dominant

6. **Identify the Required Phenotype:**
- The required phenotype (green round seeds in an inflated pod) has:
- 1 recessive trait (green seeds)
- 2 dominant traits (round seeds and inflated pod)
- The ratio for this phenotype in the F2 generation can be calculated as follows:
- The probability of getting green seeds (yy) is 1/4 (since it's recessive).
- The probability of getting round seeds (R_) is 3/4 (since it can be either RR or Rr).
- The probability of getting inflated pods (I_) is also 3/4 (since it can be either II or Ii).
- Therefore, the combined probability is:
\[ P(yyR_I) = P(yy) \times P(R_) \times P(I_) = \frac{1}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{9}{64} \]

7. **Conclusion:**
- The proportion of plants having green round seeds in an inflated pod in the F2 generation is **9/64**.