How probable is it that vertigo with no other symptoms is caused by a brain tumor?

Unlikely: Isolated vertigo is likely to be due to inflammation of the labrynth, at the inner ear.

Not too likely: A tumor on the eighth cranial nerve can occasionally cause vertigo with no other symptoms, but this is unusual. There are many other causes of vertigo which are more common than a brain tumor. Consult with your physicians and seek an appointment with an otolaryngologist (ent specialist) for diagnosis.