This clinical trial studies how well two surgical procedures (bilateral salpingectomy and bilateral salpingo-oophorectomy) work in reducing the risk of ovarian cancer for individuals with BRCA1 mutations. Bilateral salpingectomy involves the surgical removal of fallopian tubes, and bilateral salpingo-oophorectomy involves the surgical removal of both the fallopian tubes and ovaries. This study may help doctors determine if the two surgical procedures are nearly the same for ovarian cancer risk reduction for women with BRCA1 mutations.