What are the chances of getting teeth extracted and a palatal expander?

Expanded: I assume you are talking about yourself and not a child, so, in order to have room for tooth movement orthodontists many times recommend extracting some teeth to make the room. Cross bites on back teeth can be corrected by expanding the arch in children as the midline is still cartilage, adults require surgery to separate the bone for the expansion. Hope this helps.

Unlikely combination: Typically an expander is used to make space so that extractions can be avoided. Sometimes the expander is used to correct a crossbite or misfit between the two jaws, in this case it may still be necessary to have teeth removed if there is a lot of crowding.

See a pro: Please be examined by a qualified Orthodontic Specialist. Extractions required if too much tooth material for the amount of supporting bone material. Expansion (or expansion + surgery in adults) is required if upper jaw too narrow compared to lower jaw. Please see a qualified Orthodontic Specialist for advice.