A man with pure blue eyes and pure black hair marries a woman with black eyes and red hair. (black eyes are dominant over blue eyes and black hair over red hair). What will be the probabilities of phenotypes of the children?

Options

A. 50% with black eyes and black hair, and 50% blue eyes and black hair
B. All will be with black eyes and black hair
C. Both the bove cases are possible
D. `1:1:1:1`

Explanation

To solve the problem of determining the probabilities of phenotypes of the children from a man with pure blue eyes and pure black hair and a woman with black eyes and red hair, we will follow these steps:

### Step 1: Determine the Genotypes of the Parents
- The man has **pure blue eyes** and **pure black hair**.
- Blue eyes are recessive, represented as **bb** (homozygous recessive).
- Black hair is dominant, represented as **HH** (homozygous dominant).
- Therefore, the man's genotype is **bbHH**.

- The woman has **black eyes** and **red hair**.
- Black eyes are dominant, represented as **B_** (can be either homozygous dominant **BB** or heterozygous **Bb**).
- Red hair is recessive, represented as **hh** (homozygous recessive).
- Therefore, the woman's genotype can be either **BBhh** or **Bbhh**. For this problem, we will consider both cases.

### Step 2: Determine the Possible Gametes
- The man can produce gametes with the following combinations:
- From **bbHH**, the only gamete produced will be **bH**.

- For the woman, we will consider both possible genotypes:
1. If the woman is **BBhh**, she can only produce **Bh** gametes.
2. If the woman is **Bbhh**, she can produce **Bh** and **bh** gametes.

### Step 3: Perform the Punnett Square Analysis
#### Case 1: Woman is **BBhh**
- Cross the gametes:
- Man: **bH**
- Woman: **Bh**

| | Bh |
|---------|-------|
| **bH** | BbHh |

- Offspring Genotype: **BbHh** (Black eyes, Black hair)

#### Case 2: Woman is **Bbhh**
- Cross the gametes:
- Man: **bH**
- Woman: **Bh** and **bh**

| | Bh | bh |
|---------|-------|-------|
| **bH** | BbHh | bbhh |

- Offspring Genotypes:
- **BbHh** (Black eyes, Black hair)
- **bbhh** (Blue eyes, Red hair)

### Step 4: Determine the Phenotypic Ratios
- **Case 1 (Woman BBhh)**:
- 100% of children will have **Black eyes and Black hair**.

- **Case 2 (Woman Bbhh)**:
- 50% will have **Black eyes and Black hair** (BbHh).
- 50% will have **Blue eyes and Red hair** (bbhh).

### Final Probabilities of Phenotypes
- If the woman is **BBhh**: 100% Black eyes and Black hair.
- If the woman is **Bbhh**:
- 50% Black eyes and Black hair.
- 50% Blue eyes and Red hair.

### Summary
The probabilities of phenotypes of the children depend on the genotype of the mother:
- If the mother is **BBhh**: 100% Black eyes and Black hair.
- If the mother is **Bbhh**: 50% Black eyes and Black hair, 50% Blue eyes and Red hair.