Which of the following would be illegal under the fourth amendment would it be book burning, cruel, and unusual punishment, praying out loud in School, or random searches of personal property

The action that would likely be considered illegal under the Fourth Amendment is "random searches of personal property." The Fourth Amendment protects individuals from unreasonable searches and seizures by the government and requires a probable cause or a search warrant based on probable cause. Random searches without any reasonable suspicion or warrant would generally be deemed a violation of the Fourth Amendment.