Under the Fourth Amendment, which protects against unreasonable searches and seizures, the action that would be illegal is random searches of personal property. This amendment requires law enforcement to have probable cause and, in many cases, a warrant to conduct searches.
The other options listed do not fall under the scope of the Fourth Amendment:
- Book burning may have First Amendment implications related to free speech.
- Praying aloud in school can involve First Amendment issues regarding the separation of church and state.
- Cruel and unusual punishment pertains to the Eighth Amendment.
Therefore, the correct response is random searches of personal property.