Which Supreme Court decision ruled that the death penalty violated the Eighth Amendment in 1972?

The decision that ruled the death penalty violated the Eighth Amendment in 1972 is indeed Furman v. Georgia. In this landmark case, the Supreme Court addressed the issue of capital punishment and concluded that its application, as it was practiced at the time, was arbitrary and capricious. The justices found that the death penalty violated the Eighth Amendment’s prohibition against cruel and unusual punishment due to the arbitrary nature of sentencing.

The ruling effectively put a moratorium on the death penalty across the United States, arguing that it was being implemented in a discriminatory fashion, and it raised significant concerns about fairness and justice in the legal system. This decision resulted in many states re-evaluating their death penalty statutes.

The other cases listed do not relate to the death penalty or the Eighth Amendment. Roe v. Wade is centered on women's rights and abortion access, Miranda v. Arizona pertains to the rights of individuals in police custody, and Brown v. Board of Education focuses on the desegregation of public schools. Each of these cases was significant in their own right but does not address the issues surrounding the death penalty and its constitutionality.