Final answer:
The federal government finances personal health services such as Medicare and Medicaid more extensively than public health services, with entitlement programs for health being a significant part of federal spending.
Step-by-step explanation:
When comparing the federal government's role in financing personal health services to its role in financing public health services, it is evident that the federal government finances personal health services more extensively than public health services. In the United States, federal programs such as Medicare and Medicaid are prime examples of this. Medicare provides health insurance to those over the age of 65, funded by payroll taxes collected during an individual's working years. Medicaid, on the other hand, offers health coverage to low-income individuals and families, funded by government tax dollars in partnership with the states.
While the federal government does finance both personal and public health services, the scale of funding for personal health services, as seen through entitlement programs, has seen substantial growth and represents a significant portion of federal expenditure. In contrast, public health services, although funded, do not receive the same level of direct financial support when compared to personal health services.