What will be the probability of genotype TTrr in `F_2` generation of a typical Mendelian dihybrid cross ?
(a) `1//16`
(b) `3//16`
(c) `9//16`
(d) `6//16`

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 1: Understand the Parents
In a typical Mendelian dihybrid cross, we start with two parents that are homozygous for two traits. In this case, we have:
- Parent 1: TT (homozygous dominant for the first trait)
- Parent 2: rr (homozygous recessive for the second trait)

### Step 2: Determine Gametes from Parents
The gametes produced by each parent can be determined:
- Parent 1 (TT) can only produce gametes: T
- Parent 2 (rr) can only produce gametes: r

### Step 3: F1 Generation
When we cross these two parents (TT x rr), all offspring in the F1 generation will be heterozygous for the first trait and homozygous recessive for the second trait:
- F1 Generation: All offspring will be TtRr.

### Step 4: F2 Generation through Selfing
To generate the F2 generation, we self-fertilize the F1 generation (TtRr x TtRr). We can use a Punnett square to find the possible combinations of alleles.

### Step 5: Create a Punnett Square
For the traits T (dominant) and r (recessive), we can create a 4x4 Punnett square:

| | TR | Tr | tR | tr |
|----|----|----|----|----|
| **TR** | TT RR | TT Rr | Tt RR | Tt Rr |
| **Tr** | TT Rr | TT rr | Tt Rr | Tt rr |
| **tR** | Tt RR | Tt Rr | tt RR | tt Rr |
| **tr** | Tt Rr | Tt rr | tt Rr | tt rr |

### Step 6: Count the Genotypes
Now, we need to count the occurrences of the genotype TTrr:
- From the Punnett square, we see that TTrr appears once.

### Step 7: Total Combinations
The total number of combinations in the F2 generation is 16 (4 from the first trait and 4 from the second trait).

### Step 8: Calculate Probability
The probability of obtaining the genotype TTrr is the number of times it appears divided by the total combinations:
- Probability (TTrr) = Number of TTrr / Total combinations = 1/16.

### Conclusion
Thus, the probability of the genotype TTrr in the F2 generation is **1/16**.

### Answer
(a) 1/16

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