What was the major Supreme Court case regarding the legality of segregation in public schools?

The landmark Supreme Court case that addressed the legality of segregation in public schools is Brown v. Board of Education. This 1954 decision fundamentally changed the landscape of American education and civil rights. In this case, the Court unanimously ruled that racial segregation in public schools violated the Equal Protection Clause of the Fourteenth Amendment. The Court found that "separate but equal" educational facilities for racial minorities were inherently unequal, and therefore unconstitutional.

This ruling effectively overturned the precedent set by Plessy v. Ferguson in 1896, which established the "separate but equal" doctrine but primarily dealt with segregation in transportation. Brown v. Board of Education served as a catalyst for the civil rights movement, emphasizing that racial segregation cannot be justified in public education.

The other choices, while significant in their own right, do not pertain directly to the issue of segregation in public schools. Roe v. Wade is focused on abortion rights, Plessy v. Ferguson deals with public transportation and establishes the justification for segregation, and Miranda v. Arizona addresses the rights of individuals in police custody. Therefore, Brown v. Board of Education is the correct and relevant case when discussing the legality of segregation in public schools.