Pure tall pea plant with round seeds is crossed with pure dwarf pea plant with wrinkled seeds . The probability of genotype ttRR in `F_2` generation is

Options

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

Answer

To solve the problem of determining the probability of obtaining the genotype ttRR in the F2 generation from the cross of a pure tall pea plant with round seeds and a pure dwarf pea plant with wrinkled seeds, we can follow these steps:

### Step 1: Determine the Genotypes of the Parent Plants
- The pure tall pea plant with round seeds has the genotype **TTRR** (homozygous tall and homozygous round).
- The pure dwarf pea plant with wrinkled seeds has the genotype **ttrr** (homozygous dwarf and homozygous wrinkled).

### Step 2: Determine the Gametes Produced by Each Parent
- The tall round plant (TTRR) can only produce one type of gamete: **TR**.
- The dwarf wrinkled plant (ttrr) can only produce one type of gamete: **tr**.

### Step 3: Perform the F1 Cross
- When we cross TTRR with ttrr, the F1 generation will have the genotype **TtRr** (heterozygous tall and heterozygous round). The phenotype will be tall and round.

### Step 4: Self-Fertilization of F1 Generation
- The F1 plants (TtRr) will self-fertilize to produce the F2 generation. We need to determine the possible gametes from TtRr.
- The gametes produced by TtRr will be: **TR, Tr, tR, tr**.

### Step 5: Create a Punnett Square for F2 Generation
- Set up a 4x4 Punnett square using the gametes from both parents:
```
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: Identify the Desired Genotype
- We are looking for the genotype **ttRR**. From the Punnett square, we can see that **ttRR** appears only once in the entire square.

### Step 7: Calculate the Probability
- There are a total of 16 possible genotypes in the F2 generation (4x4 Punnett square).
- The genotype **ttRR** occurs 1 time out of 16 total combinations.

### Final Answer
- The probability of obtaining the genotype **ttRR** in the F2 generation is **1/16**.

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