What is the probability of homozygous plants for both dominant characters in `F_(2)` generation of a dihybrid cross :-

Options

A. `1//16`
B. `3//16`
C. `4//16`
D. `9//16`

Answer

To determine the probability of homozygous plants for both dominant characters in the F2 generation of a dihybrid cross, we can follow these steps:

### Step 1: Understand the Dihybrid Cross
In a dihybrid cross, we are examining two traits, each with two alleles. For example, let's consider:
- Trait 1: Seed shape (Round - R is dominant, Wrinkled - r is recessive)
- Trait 2: Seed color (Yellow - Y is dominant, Green - y is recessive)

### Step 2: Identify the Parental Generation
The parental generation consists of:
- Round Yellow (RRYY) x Wrinkled Green (rryy)

### Step 3: Determine the F1 Generation
The F1 generation will all be heterozygous for both traits:
- All offspring will be RrYy (Round Yellow).

### Step 4: Perform the F2 Generation Cross
To obtain the F2 generation, we cross two F1 individuals:
- RrYy x RrYy

### Step 5: Create a Punnett Square
A 4x4 Punnett square can be used to determine the genotypes of the F2 generation. The combinations of alleles will be:
- RY, Ry, rY, ry (from one parent)
- RY, Ry, rY, ry (from the other parent)

### Step 6: Count the Genotypes
Filling in the Punnett square, we get the following combinations:
1. RRYY
2. RRYy
3. RrYY
4. RrYy
5. RRYy
6. Rryy
7. rrYY
8. rrYy
9. RrYy
10. Rryy
11. rrYy
12. rryy
13. RrYY
14. RRYy
15. rrYY
16. rryy

### Step 7: Identify Homozygous Dominant Plants
From the combinations, the homozygous dominant genotype for both traits is:
- RRYY

### Step 8: Calculate the Probability
Out of the 16 total combinations, only 1 is homozygous for both dominant traits (RRYY). Therefore, the probability is:
- Probability = Number of homozygous dominant plants / Total plants = 1/16

### Conclusion
The probability of homozygous plants for both dominant characters in the F2 generation of a dihybrid cross is **1/16**.

### Final Answer
The correct answer is **1 is to 16**.

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