The grandsons of a colour blind male through daughter having the following probability of being colour blind is

Options

A. 0
B. 0.5
C. 0.25
D. 0.125

Answer

To solve the problem of determining the probability of the grandsons of a colorblind male being colorblind, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Genetics of Colorblindness**:
- Colorblindness is a sex-linked recessive trait, which means it is carried on the X chromosome. Males (XY) have one X chromosome, while females (XX) have two.

2. **Identify the Genotype of the Colorblind Male**:
- The colorblind male has the genotype X^cY, where X^c represents the X chromosome with the colorblind allele.

3. **Determine the Genotype of the Daughter**:
- The daughter of the colorblind male must inherit one X chromosome from him (X^c) and one X chromosome from her mother (who can either be normal (X) or a carrier (X^c)).
- Therefore, the daughter can have the following genotypes:
- If the mother is normal (XX): the daughter will be X^cX (carrier).
- If the mother is a carrier (X^cX): the daughter can be X^cX (carrier) or XX (normal).

4. **Probability of the Daughter's Genotype**:
- If we assume the mother is a carrier (X^cX), there is a 50% chance the daughter will be a carrier (X^cX) and a 50% chance she will be normal (XX).

5. **Determine the Genotype of the Grandsons**:
- The grandsons will inherit their X chromosome from their mother (the daughter).
- If the daughter is X^cX (carrier), she can pass on either X^c (colorblind) or X (normal) to her sons.
- If the daughter is XX (normal), she can only pass on X (normal) to her sons.

6. **Calculate the Probability of Grandsons Being Colorblind**:
- If the daughter is a carrier (X^cX), there is a 50% chance for each grandson to be colorblind (X^cY).
- If the daughter is normal (XX), there is a 0% chance for each grandson to be colorblind.
- Therefore, if we assume the mother is a carrier, the probability of grandsons being colorblind is 0.5 (50%).

7. **Final Probability Calculation**:
- Since we need to consider the probability of the daughter being a carrier, the overall probability of the grandsons being colorblind is:
- Probability of daughter being a carrier (0.5) * Probability of grandsons being colorblind if daughter is a carrier (0.5) = 0.5 * 0.5 = 0.25.

### Conclusion:
The probability of the grandsons of a colorblind male being colorblind is **0.25** (or 25%).

### Answer:
Option C: 0.25