Raj having genotype AaBBCc for skin colour marries simran having genotype AAbbCc for skin colour . What is the change 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 probability that Raj and Simran have a child whose skin color does not match either of their skin colors, we need to analyze their genotypes and the possible combinations of alleles they can produce in their offspring.

### Step-by-Step Solution:

1. **Identify the Genotypes**:
- Raj's genotype: AaBBCc
- Simran's genotype: AAbbCc

2. **Determine the Gametes Produced**:
- Raj can produce the following gametes:
- From A (Aa): A, a
- From B (BB): B (only one type since it is homozygous)
- From C (Cc): C, c
- Thus, the possible gametes from Raj are:
- ABC
- ABc
- aBC
- aBc

- Simran can produce the following gametes:
- From A (AA): A (only one type since it is homozygous)
- From B (bb): b (only one type since it is homozygous)
- From C (Cc): C, c
- Thus, the possible gametes from Simran are:
- AbC
- Abc

3. **Cross the Gametes**:
- Now, we will cross the gametes from Raj and Simran to find the possible genotypes of their children:
- Raj's gametes: ABC, ABc, aBC, aBc
- Simran's gametes: AbC, Abc

- The combinations will be:
1. ABC x AbC = AABBCc
2. ABC x Abc = AABbCc
3. ABc x AbC = AABBCc
4. ABc x Abc = AABbCc
5. aBC x AbC = AaBBCc
6. aBC x Abc = AaBbCc
7. aBc x AbC = AaBBCc
8. aBc x Abc = AaBbCc

4. **Identify Unique Genotypes**:
- The unique genotypes from the combinations are:
1. AABBCc
2. AABbCc
3. AaBBCc
4. AaBbCc

5. **Determine Skin Color**:
- Raj has the genotype AaBBCc, which has a combination of 4 dominant alleles (A, B, C).
- Simran has the genotype AAbbCc, which has a combination of 3 dominant alleles (A, B, C).
- A child with skin color that does not match either parent would need to have a different combination of dominant and recessive alleles.

6. **Count Non-Matching Genotypes**:
- The genotypes that do not match either parent are:
- AABbCc (3 dominant alleles)
- AaBbCc (2 dominant alleles)
- Therefore, there are 2 out of 8 possible combinations that do not match either parent.

7. **Calculate the Probability**:
- The probability of having a child whose skin color does not match either Raj's or Simran's is:
\[ \text{Probability} = \frac{\text{Number of Non-Matching Genotypes}}{\text{Total Genotypes}} = \frac{2}{8} = 0.25 \text{ or } 25\% \]

### Final Answer:
The probability that Raj and Simran have a child whose skin color does not match either of theirs is **25%**.