Is Uterus Removal Needed Due To Large Cyst On Fallopian Tubes?

I am 53 yrs. 5'6" and weigh 140Lbs. I have never had any major Operations. I have had two children and no pregnancy problems. I have a large cyst on one of my Fallopian Tubes and the Dr. recommends getting both removed because of a 20% chance of getting the same thing on the other one. I am through menopause and don't have a problem with that. My question is; should I also have the Uterus and Ovaries removed?