Final answer:
The patient is likely to have Acute myeloid leukemia (AML), characterized by an overproduction of young, immature leukocytes. AML is associated with high leukocyte count, presence of late neutrophil precursors, and high alkaline phosphatase.
Step-by-step explanation:
The patient with a leukocyte count > 50,000 and high alkaline phosphatase score, and a greater proportion of late neutrophil precursors is likely to have Acute myeloid leukemia (AML).
AML is a type of leukemia that involves an overproduction of young, immature leukocytes. The high leukocyte count, along with the presence of late neutrophil precursors and high alkaline phosphatase, are characteristic of AML.
In AML, the cells do not function properly and there is impaired production of erythrocytes and other blood cells.