Raj having genotype AaBBCc for skin colour marries simran having genotype AAbbCc for skin colour . What is the chance that they have a child whose skin colour doesn't match with either Raj's or Simran 's ?

Options

A. `12.5%`
B. `16.67%`
C. `25%`
D. `50%`

Answer

To solve the problem of determining the chance that Raj and Simran have a child whose skin color does not match either of their skin colors, we will follow these steps:

### Step 1: Identify the Genotypes
Raj's genotype is AaBBCc, and Simran's genotype is AAbbCc.

### Step 2: Determine the Dominant Alleles
From Raj's genotype (AaBBCc), the dominant alleles are A, B, and C. From Simran's genotype (AAbbCc), the dominant alleles are A, B, and C as well.

### Step 3: Identify Possible Gametes
To find the gametes produced by each parent, we will consider the combinations of alleles they can pass on:

- **Raj's Gametes**:
- From Aa: A or a
- From BB: B (only one possibility)
- From Cc: C or c
- Possible gametes: ABc, ABc, AbC, Abc (4 types)

- **Simran's Gametes**:
- From AA: A (only one possibility)
- From bb: b (only one possibility)
- From Cc: C or c
- Possible gametes: AbC, Abc (2 types)

### Step 4: Perform the Cross
Now we will cross the gametes from both parents:

| Raj's Gametes | Simran's Gametes | Offspring Genotypes |
|---------------|------------------|---------------------|
| ABC | ABc | AABBCc |
| ABC | AbC | AABBCc |
| ABc | ABc | AABbCc |
| ABc | AbC | AABbCc |
| AbC | ABc | AaBBCc |
| AbC | AbC | AaBbCc |
| Abc | ABc | AaBBCc |
| Abc | AbC | AaBbCc |

### Step 5: Count the Offspring Genotypes
From the combinations, we can see the following offspring genotypes:
1. AABBCc
2. AABbCc
3. AaBBCc
4. AaBbCc

### Step 6: Determine the Matching Skin Colors
- Raj has genotype AaBBCc (dominant alleles: A, B, C).
- Simran has genotype AAbbCc (dominant alleles: A, B).

For a child to not match either parent, they must have at least one recessive allele for each trait. This means they must have:
- At least one 'a' (from A)
- At least one 'b' (from B)
- At least one 'c' (from C)

### Step 7: Calculate the Probability
Now we need to find how many of the offspring genotypes do not match either parent.

From the offspring genotypes listed, we can see that:
- None of the offspring genotypes have a combination of recessive alleles for all three traits (a, b, c).

Thus, the chance that they have a child whose skin color does not match either Raj's or Simran's is 0%.

### Final Answer
The chance that Raj and Simran have a child whose skin color does not match either of their skin colors is **0%**.

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