Pure tall purple variety of pea plant was crossed with dwarf white plant. What is the probability of getting phenotypes tall purple in `F_(2)` generation

Options

A. `(3)/(16)`
B. `(1)/(2)`
C. `(9)/(16)`
D. `(4)/(16)`

Answer

To solve the problem of determining the probability of getting the phenotypes tall purple in the F2 generation from a cross between a pure tall purple pea plant and a dwarf white pea plant, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parental Genotypes:**
- The pure tall purple plant can be represented as TT (homozygous tall) and PP (homozygous purple).
- The dwarf white plant can be represented as tt (homozygous dwarf) and pp (homozygous white).

2. **Determine the F1 Generation:**
- When we cross the two parental plants, the F1 generation will have the genotype TtPp (heterozygous for both traits).
- All F1 plants will exhibit the dominant phenotypes, which are tall (T) and purple (P).

3. **Selfing the F1 Generation:**
- To find the F2 generation, we will perform a self-cross of the F1 plants (TtPp x TtPp).
- We will use a Punnett square to determine the possible genotypes in the F2 generation.

4. **Gamete Formation:**
- The gametes from each F1 plant can be: TP, Tp, tP, tp.
- Therefore, the F2 generation will result from the combination of these gametes.

5. **Constructing the Punnett Square:**
- Create a 4x4 Punnett square using the gametes:
```
TP Tp tP tp
---------------------
TP | TT PP | TT Pp | Tt PP | Tt Pp |
---------------------
Tp | TT Pp | TT pp | Tt Pp | Tt pp |
---------------------
tP | Tt PP | Tt Pp | tt PP | tt Pp |
---------------------
tp | Tt Pp | Tt pp | tt Pp | tt pp |
---------------------
```

6. **Counting the Phenotypes:**
- From the Punnett square, we can count the phenotypes:
- Tall Purple (T_P): TT PP, TT Pp, Tt PP, Tt Pp (9 total)
- Tall White (T_pp): TT pp, Tt pp (3 total)
- Dwarf Purple (tt P_): tt PP, tt Pp (3 total)
- Dwarf White (tt pp): tt pp (1 total)

7. **Calculating the Probability:**
- The total number of plants is 16.
- The number of tall purple plants is 9.
- Therefore, the probability of getting tall purple plants in the F2 generation is 9/16.

### Final Answer:
The probability of getting phenotypes tall purple in the F2 generation is **C) 9/16**.