A roan bull is bread to three cows. Cow A has the same genotype as the roan bull. Cow B is red and cow C is white. What proportiions of roan cows are expected in the offsprings of each group of cows :-

Options

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

Answer

To solve the problem of determining the expected proportions of roan cows in the offspring of a roan bull bred to three different cows (Cow A, Cow B, and Cow C), we will follow these steps:

### Step 1: Understand the Genotypes
- The roan bull has the genotype **Ww** (where **W** represents red and **w** represents white).
- Cow A, which has the same genotype as the roan bull, also has the genotype **Ww**.
- Cow B is red, so its genotype is **WW**.
- Cow C is white, so its genotype is **ww**.

### Step 2: Cross the Genotypes
1. **Cross between Roan Bull (Ww) and Cow A (Ww)**:
- Possible gametes from both parents:
- Roan Bull: W, w
- Cow A: W, w
- Punnett Square:
```
W | w
----------------
W | WW | Ww
----------------
w | Ww | ww
```
- Offspring genotypes: WW, Ww, Ww, ww
- Phenotypic ratio: 1 Red (WW): 2 Roan (Ww): 1 White (ww)
- Proportion of roan cows = 2 out of 4 = **1/2** or **50%**.

2. **Cross between Roan Bull (Ww) and Cow B (WW)**:
- Possible gametes:
- Roan Bull: W, w
- Cow B: W, W
- Punnett Square:
```
W | W
----------------
W | WW | WW
----------------
w | Ww | Ww
```
- Offspring genotypes: WW, WW, Ww, Ww
- Phenotypic ratio: 2 Red (WW): 2 Roan (Ww)
- Proportion of roan cows = 2 out of 4 = **1/2** or **50%**.

3. **Cross between Roan Bull (Ww) and Cow C (ww)**:
- Possible gametes:
- Roan Bull: W, w
- Cow C: w, w
- Punnett Square:
```
W | w
----------------
w | Ww | w
----------------
w | Ww | w
```
- Offspring genotypes: Ww, Ww, ww, ww
- Phenotypic ratio: 2 Roan (Ww): 2 White (ww)
- Proportion of roan cows = 2 out of 4 = **1/2** or **50%**.

### Step 3: Summarize the Results
- Proportion of roan cows expected from:
- Cow A: **1/2** (50%)
- Cow B: **1/2** (50%)
- Cow C: **1/2** (50%)

### Final Answer
The proportions of roan cows expected in the offspring of each group of cows are:
- Cow A: 50%
- Cow B: 50%
- Cow C: 50%

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