Additional Study Information: The main purpose of this study is to determine if two surgical procedures, the usual approach of removing the fallopian tubes and ovaries and the other approach of removing the fallopian tubes at this time with the plan to remove the ovaries at a later time, are no different for ovarian cancer risk reduction in women with BRCA1 mutations who have completed childbearing. In this study, the removal of fallopian tubes will be compared to the removal of fallopian tubes and ovaries. The study will also examine what factors go into deciding which surgery to have and symptoms after surgery caused by lack of estrogen due to ovary removal.