All of the options listed (Education, Public aid, Libraries, and Corrections) are major responsibilities of state governments. Therefore, there is no option that is not one of the major responsibilities of state government.
State governments are responsible for a wide range of functions and services, including but not limited to:
Education: State governments are responsible for providing and funding public K-12 schools, as well as overseeing higher education institutions within their state.
Public aid: State governments provide a range of public assistance programs, such as Medicaid, food stamps, and cash assistance for low-income families.
Libraries: State governments may fund and operate public libraries within their state.
Corrections: State governments are responsible for maintaining and operating correctional facilities, such as prisons and jails, and overseeing probation and parole programs for those who have been convicted of crimes.
These functions are just a few examples of the many responsibilities that state governments have in providing services to their citizens.