Final answer:
State Medicaid is the suitable insurance for a single mother unable to work, with three children. It provides health care for those with low incomes and has been expanded to cover the near-poor and ensure children do not lose coverage if their parents work.
Step-by-step explanation:
The insurance form most appropriate for a single mother who is unable to work and has three children would be State Medicaid. Understanding the distinct roles of different types of insurance is crucial, both at an individual and policy level. Medicaid is designed to provide health care to those with low incomes, which would typically apply to a mother without a working income and with dependent children. Private health insurance, typically too expensive for low-income families, would not be a suitable option in this scenario. Additionally, Federal Medicare targets individuals over the age 65 and not the population in question here.
The federal government along with state participation ensures that Medicaid assists not just the poor but potentially those earning slightly above the poverty line, including the near-poor. This expansion ensures that even if the mother or future caregivers find low-paying jobs, the children's health coverage is not put at risk, and thereby helps to avoid the 'poverty trap' where individuals refrain from employment to retain health insurance benefits for their family.