What will be the probability of genotype TTrr in `F_2` generation of a typical Mendelian dihybrid cross ?

Options

A. `1//16`
B. `3//16`
C. `9//16`
D. `6//16`

Answer

To find the probability of the genotype TTRR in the F2 generation of a typical Mendelian dihybrid cross, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Parent Genotypes**:
In a typical Mendelian dihybrid cross, we start with two parent plants. For this example, let's assume the first parent has the genotype TTRR (tall plant with red flowers) and the second parent has the genotype ttrr (dwarf plant with white flowers).

2. **Determine the F1 Generation**:
When we cross TTRR (homozygous dominant) with ttrr (homozygous recessive), all offspring in the F1 generation will have the genotype TtRr. This is because each parent contributes one allele for each trait.

3. **Cross the F1 Generation to Obtain F2 Generation**:
To obtain the F2 generation, we need to cross two F1 individuals (TtRr x TtRr).

4. **Set Up a Punnett Square**:
We can set up a 4x4 Punnett square to determine the possible genotypes of the F2 generation. The gametes from each TtRr parent will be TR, Tr, tR, and tr.

5. **Calculate the Total Genotypes**:
When we fill in the Punnett square, we will find a total of 16 possible genotype combinations in the F2 generation.

6. **Identify the Desired Genotype**:
We are interested in the genotype TTRR. From the Punnett square, we can count how many times TTRR appears.

7. **Count the Occurrences**:
In the F2 generation, TTRR appears once among the 16 total genotypes.

8. **Calculate the Probability**:
The probability of obtaining the genotype TTRR is the number of times TTRR appears divided by the total number of genotypes. Thus, the probability is 1/16.

### Final Answer:
The probability of the genotype TTRR in the F2 generation of a typical Mendelian dihybrid cross is **1/16**.

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