Final answer:
William's medical expenses in a nursing home would primarily be covered by Medicare, a program for those over 65, and possibly supplemented by Medicaid, which helps low-income Americans.
Step-by-step explanation:
The medical expenses of sixty-two-year-old William, who is a retired employee staying in a nursing home, are most likely to be covered by Medicare, which provides health insurance to individuals over the age of 65.
Given that the nursing home caters to low-income individuals, William's expenses may also be supplemented by Medicaid, which assists low-income Americans of all ages with their medical costs, including the costs for nursing home care. It is important to note that while Medicare is a federal program providing primarily for the elderly, Medicaid varies by state regarding eligibility and benefits.