Hi Julia. This is a topic that I would recommend doing some research on, because the answer is dependent upon a number of things - how old the person with the AVM is, where the AVM is located, etc.
You may be interested in some answers to a similar post:
http://www.avmsurvivors.org/forum/topics/are-avms-hereditary
In my case the doctors told me that mine was inherited, and I was told by relatives about
an uncle who had suffered a cerebral bleed a generation ago and had died from it.