The ratio of the number of kinds of double homozygous to double heterozygous to single homozygous genotypes of `F_(2)` generation of a Mendelian dihybrid cross is

Options

A. `1:4:4`
B. `4:4:1`
C. `4:1:4`
D. `4:2:3`

Answer

To solve the problem regarding the ratio of the number of kinds of double homozygous to double heterozygous to single homozygous genotypes in the F2 generation of a Mendelian dihybrid cross, we can follow these steps:

### Step 1: Understand the Genotypes
In a Mendelian dihybrid cross, we are dealing with two traits, each represented by two alleles. Let's denote the traits as follows:
- Trait 1 (e.g., height): T (tall) and t (short)
- Trait 2 (e.g., color): B (black) and b (white)

### Step 2: Identify the Types of Genotypes
1. **Double Homozygous Genotypes**: These are genotypes where both traits are homozygous.
- Possible combinations:
- TTBB (tall and black)
- TTBb (tall and heterozygous for color)
- ttBB (short and black)
- ttBb (short and heterozygous for color)
- Total types of double homozygous: 4

2. **Double Heterozygous Genotype**: This is where both traits are heterozygous.
- Possible combination:
- TtBb (tall and heterozygous for color)
- Total types of double heterozygous: 1

3. **Single Homozygous Genotypes**: These are genotypes where one trait is homozygous and the other is heterozygous.
- Possible combinations:
- TTBb (tall and heterozygous for color)
- TtBB (heterozygous for height and black)
- TtBb (heterozygous for both)
- ttBb (short and heterozygous for color)
- ttBB (short and black)
- Total types of single homozygous: 4

### Step 3: Calculate the Ratio
Now that we have identified the types of genotypes:
- Double Homozygous: 4
- Double Heterozygous: 1
- Single Homozygous: 4

Thus, the ratio of double homozygous to double heterozygous to single homozygous is:
\[ 4 : 1 : 4 \]

### Step 4: Conclusion
The answer to the question is that the ratio of the number of kinds of double homozygous to double heterozygous to single homozygous genotypes in the F2 generation of a Mendelian dihybrid cross is **4:1:4**.