Can you catch mumps if you have been fully vaccinated? what is the likely hood?

Yes, it depends: The mumps vaccine isn't all that effective; after a single dose about 75% of people are protected; after a second dose about 85% are protected. But this does not mean there is a 15% chance of getting mumps as one first has to be exposed which is unlikely. But even if one gets mumps it's generally a mild, benign self-limited illness. Women who have had mumps have a lower risk of ovarian cancer!

Mumps : Mumps vaccine gives 75-85 % protection . So theoretically there is chance of catching mumps infection.