Final answer:
The case that established police can search automobiles without a search warrant given probable cause is Carroll v. United States.
Step-by-step explanation:
The case that allowed police to search automobiles upon probable cause but without a search warrant is C) Carroll v. United States. This landmark decision established that the mobility of an automobile provides an exception to the Fourth Amendment requirement of a search warrant, albeit still requiring probable cause for a search to be lawful. This exception is predicated on the exigent circumstances that a vehicle can quickly be moved out of the jurisdiction.