In which condition would an elevated serum alkaline phosphatase be likely to occur?

An elevated serum alkaline phosphatase is most commonly associated with conditions that involve biliary tract obstruction, bone diseases, or conditions that affect the liver. In the case of small cell lung carcinoma, although it primarily affects the lungs, it can also lead to paraneoplastic syndromes or metastatic spread that affects the liver or bone. This can result in elevated alkaline phosphatase levels due to bone involvement or liver dysfunction.

In contrast, the conditions listed in the other choices do not typically lead to an increase in alkaline phosphatase. For example, prostate cancer may lead to an elevation in prostate-specific antigen (PSA) rather than alkaline phosphatase directly. Hemolytic anemia primarily affects red blood cell counts and lysis but does not directly cause increased alkaline phosphatase. Acute myocardial infarction mainly pertains to cardiac enzyme elevation rather than affecting alkaline phosphatase levels significantly.

Thus, small cell lung carcinoma stands out as the condition where elevated serum alkaline phosphatase would be likely, reflecting its potential effects on bone or liver function during the course of the disease.