If someone gets MRSA will they be cured by antibiotic or will tthey become a carrier of it.?

Maybe. Mrsa or methicillin resistant staph aureus is a antibiotic resistant bacteria. By definition it is more difficult to treat than a non resistant bacteria. A simple course of antibiotics will not treat the bacteria living on the skin. Some have recommended Mupirocin ointment to the nose in conjunction with chlorohexadine baths, however results for this have been mixed. Discuss with a doctor.