In a cross between plants with purple flowers and plants with white flowers, the offspring of `F_1` generation all had white flowers. When the `F_1` generation was self-crossed, it was observed in the `F_2` generation that out of 100, 75 flowers were white. Make a cross and answer the following questions:
The ratio of 'White: generation is Purple' flowers in the `F_2`
a) `3 : 1`
b) `1 :2`
c) `1:3`
d) ` 2:1`

Options

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

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the Parent Plants
We have two types of plants:
- **Purple flowers (P)**: Let's denote this as "P" (homozygous recessive).
- **White flowers (W)**: Let's denote this as "W" (homozygous dominant).

### Step 2: Determine the Genotypes of the Parents
- The genotype of the purple flower plant is **PP** (homozygous dominant).
- The genotype of the white flower plant is **WW** (homozygous recessive).

### Step 3: Cross the Parent Plants to Get F1 Generation
When we cross these two plants (PP x WW), all offspring in the F1 generation will have the genotype **PW**. Since white (W) is dominant over purple (P), all F1 plants will exhibit the white flower phenotype.

### Step 4: Self-Cross the F1 Generation
Now, we self-cross the F1 generation plants (PW x PW). We can set up a Punnett square to determine the genotypes of the F2 generation.

### Step 5: Create the Punnett Square
The Punnett square for the self-cross of PW x PW will look like this:

```
P W
----------------
P | PP | PW |
----------------
W | PW | WW |
----------------
```

### Step 6: Determine the Genotypes and Phenotypes of F2 Generation
From the Punnett square, we can see:
- **PP**: 1 (Purple flowers)
- **PW**: 2 (White flowers)
- **WW**: 1 (White flowers)

### Step 7: Count the Phenotypes
In total, we have:
- **White flowers**: 3 (2 from PW + 1 from WW)
- **Purple flowers**: 1 (from PP)

### Step 8: Calculate the Ratio
The ratio of white to purple flowers in the F2 generation is:
- White: 3
- Purple: 1

Thus, the ratio of white to purple flowers is **3:1**.

### Final Answer
The answer to the question is:
**a) 3:1**

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