**Core Concept:**
Autosomal Recessive Genetics: In this question, we are discussing the inheritance pattern of autosomal recessive genes. Autosomal genes are those that are not sex-linked and are inherited from both parents. In autosomal recessive inheritance, an individual must inherit two copies of the mutated gene (one from each parent) to be affected by the disease. If both parents are carriers (heterozygous), the chances of different outcomes depend on the genotypes of the parents and the offspring.

**Why the Correct Answer is Right:**
The correct answer explains the potential outcomes based on the genotypes of the parents and the offspring. In this case, the first child is heterozygous (carrier) for the autosomal recessive gene, while the wife is homozygous for the same gene. A homozygous individual has two copies of the mutated gene, while a heterozygous individual has one normal gene and one mutated gene.

**Why Each Wrong Option is Incorrect:**
A. This option is incorrect because a homozygous individual (homozygous recessive) would also be a carrier, not affected by the disease.
B. This option is incorrect because a heterozygous individual (heterozygous) can give birth to a carrier child, but not to an affected child.
C. This option is incorrect as it describes the outcome for a homozygous recessive couple, rather than the heterozygous couple in the question.
D. This option is incorrect because it describes the outcome for a homozygous dominant couple, which is not relevant to the given scenario.

**Clinical Pearl:**
When a heterozygous individual (carrier) mates with a homozygous recessive individual, the possible outcomes are:

1. The child could be a heterozygous carrier (A) or a homozygous recessive (C), both of which are not affected by the disease.
2. The child could be affected by the disease (D), which is not relevant to the given scenario.

**Correct Answer:**
Correct Answer: A. The first child could be a heterozygous carrier (carrier) or a homozygous recessive (carrier), both of which are not affected by the disease.

Explanation: In this scenario, the child inherits one normal gene from the father and one mutated gene from the mother. The child will be a heterozygous carrier, meaning they have one normal gene and one mutated gene. They will not be affected by the disease but can pass on the mutated gene to their offspring.