**Core Concept**
Thalassemia trait is a genetic disorder characterized by reduced production of hemoglobin, leading to mild anemia. Confirming the diagnosis involves identifying the specific genetic mutations responsible for the condition.

**Why the Correct Answer is Right**
Hemoglobin electrophoresis is a laboratory test used to separate and identify different types of hemoglobin in the blood. In a patient with a positive family history of thalassemia, hemoglobin electrophoresis is the most reliable method to confirm the diagnosis of thalassemia trait by detecting the presence of abnormal hemoglobin variants, such as HbA2 or HbF. This test is particularly useful in individuals with a family history of the condition, as it can help identify carriers of the mutation.

**Why Each Wrong Option is Incorrect**
**Option A:** Complete Blood Count (CBC) is a basic test that provides an overview of various blood cell parameters but does not specifically diagnose thalassemia trait. It may show mild anemia, but the results are non-specific and not diagnostic.
**Option B:** Serum iron levels can be affected in thalassemia due to chronic anemia but are not a reliable method for confirming the diagnosis of thalassemia trait.
**Option C:** Bone marrow examination can provide information about the production of blood cells but is not a specific or practical test for diagnosing thalassemia trait.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that hemoglobin electrophoresis is the gold standard for diagnosing thalassemia trait, especially in individuals with a family history of the condition. This test helps identify carriers of the mutation, which is essential for genetic counseling and family planning.

**Correct Answer: C. Hemoglobin electrophoresis.**