Final answer:
Officer Olga relied on the exception established in the New Jersey v. T. L. O. case, which allows public school officials to conduct searches based on reasonable suspicion rather than probable cause.
Step-by-step explanation:
The exception to the Fourth Amendment that Officer Olga relied on is the New Jersey v. T. L. O. case. This case established that the Fourth Amendment's ban on unreasonable searches applies to public school officials, but they can use a less strict standard of reasonable suspicion instead of probable cause. In this case, school officials conducted a search of a student's purse based on suspicion of having cigarettes, which led to the discovery of marijuana and evidence of drug distribution.