A man & women who both appear normal have a child together, who has sickle cell anaemia. The woman becomes pregnant again and is told that she is carrying fraternal (dizygotic) twins. What is the probability that both of the couple's twins will have Sickle Cell Anaemia :-

Options

A. `(1)/(16)`
B. `(1)/(4)`
C. `(1)/(2)`
D. `(9)/(16)`

Answer

To solve the problem of determining the probability that both of the couple's fraternal twins will have sickle cell anemia, we can follow these steps:

### Step 1: Understand the Genetics of Sickle Cell Anemia
Sickle cell anemia is an autosomal recessive disorder. This means that an individual must inherit two copies of the sickle cell gene (HbS) to express the disease. The normal gene is represented as HbA, while the sickle cell gene is represented as HbS.

### Step 2: Determine the Genotypes of the Parents
The couple appears normal but has a child with sickle cell anemia. This indicates that both parents are carriers of the sickle cell trait. Therefore, their genotypes are:
- Father: HbA HbS (carrier)
- Mother: HbA HbS (carrier)

### Step 3: Create a Punnett Square
To find the possible genotypes of their offspring, we can set up a Punnett square using the parents' genotypes:

| | HbA | HbS |
|-------|-----|-----|
| **HbA** | HbA HbA | HbA HbS |
| **HbS** | HbA HbS | HbS HbS |

### Step 4: Analyze the Offspring Genotypes
From the Punnett square, the possible genotypes of the offspring are:
- HbA HbA (normal) - 1 out of 4
- HbA HbS (carrier) - 2 out of 4
- HbS HbS (sickle cell anemia) - 1 out of 4

Thus, the probability of an offspring having sickle cell anemia (HbS HbS) is 1 out of 4, or 25%.

### Step 5: Calculate the Probability for Fraternal Twins
Since the couple is having fraternal (dizygotic) twins, the probability of each twin being affected is independent of the other. Therefore, we multiply the probabilities for each twin:

Probability that Twin 1 has sickle cell anemia = 1/4
Probability that Twin 2 has sickle cell anemia = 1/4

Thus, the probability that both twins have sickle cell anemia is:
\[ \text{Probability} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{16} \]

### Conclusion
The probability that both of the couple's fraternal twins will have sickle cell anemia is **1/16**.

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