**Core Concept**
The child presented with a valgus deformity at the elbow, which is likely due to a previous fracture that has led to growth disturbance in the affected limb. This condition is associated with an abnormal growth pattern in the distal humerus, leading to a valgus deformity.

**Why the Correct Answer is Right**
The probable fracture responsible for this valgus deformity is a supracondylar fracture of the humerus. This type of fracture occurs just above the elbow joint and can lead to growth disturbances if not properly managed. The fracture may have occurred 3 years ago when the child fell on an outstretched hand, leading to a cast being applied for 6 weeks. However, the growth plate in the distal humerus may have been affected, leading to an abnormal growth pattern and valgus deformity.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not relevant to the child's presentation. A medial epicondylar fracture is a different type of fracture that occurs at the medial aspect of the elbow and is not associated with growth disturbances.
* **Option B:** This option is not correct. A lateral condyle fracture of the humerus can lead to a varus deformity, not a valgus deformity.
* **Option D:** This option is not relevant to the child's presentation. A fracture of the olecranon is a different type of fracture that occurs at the tip of the elbow and is not associated with growth disturbances.

**Clinical Pearl / High-Yield Fact**
A supracondylar fracture of the humerus can lead to growth disturbances if not properly managed, resulting in valgus or varus deformities. This highlights the importance of early and accurate diagnosis, as well as proper management of childhood fractures to prevent long-term complications.

**Correct Answer:** C. Supracondylar fracture of the humerus.