Final answer:
The U.S. Supreme Court ruling that allows a warrantless search of a vehicle with probable cause is known as the Carroll doctrine.
Step-by-step explanation:
The U.S. Supreme Court ruling that permits a warrantless search of a vehicle with probable cause is known as the Carroll doctrine. The Carroll doctrine, established in 1925 with the case Carroll v. United States, allows police to search a vehicle without a warrant as long as they have reasonable belief that the car contains evidence of a crime. This exception to the warrant requirement is based on the mobility of vehicles and the reduced expectation of privacy in a car compared to a home or personal property.