**Core Concept**
Osteogenesis imperfecta is a genetic disorder characterized by brittle bones, often due to mutations in the COL1A1 or COL1A2 genes, which encode type I collagen. The disorder follows an autosomal dominant pattern of inheritance, meaning a single copy of the mutated gene is sufficient to cause the condition.

**Why the Correct Answer is Right**
In an autosomal dominant pattern, each child of an affected parent has a 50% chance of inheriting the mutated gene. This means that even if a parent has only one copy of the mutated gene, they can still pass it on to their offspring. Since the parent in question has osteogenesis imperfecta, it is likely that they have an autosomal dominant mutation, and therefore, each child has a 50% chance of inheriting the disorder.

**Why Each Wrong Option is Incorrect**
* **Option B:** Autosomal recessive inheritance would require both parents to be carriers of the mutated gene, which is not the case here since the parent has the disorder.
* **Option C:** X-linked dominant inheritance would be more common in females, as they have two X chromosomes, but this is not the case here.
* **Option D:** Mitochondrial inheritance would be passed down from the mother only, but osteogenesis imperfecta is not typically associated with mitochondrial inheritance.

**Clinical Pearl / High-Yield Fact**
Autosomal dominant disorders often have a high penetrance, meaning that individuals who inherit the mutated gene will likely develop the condition. It's essential to consider the pattern of inheritance when counseling families about genetic disorders.

**Correct Answer:** C.