Carboplatin and Paclitaxel With or Without Bevacizumab in Treating Patients With Stage III or Stage IV Ovarian Epithelial, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Patients with a histologic diagnosis of epithelial ovarian cancer, peritoneal primary carcinoma or fallopian tube cancer; International Federation of Gynecology and Obstetrics (FIGO) stage III with any gross (macroscopic or palpable) residual disease or FIGO stage IV, defined surgically at the completion of initial abdominal surgery and with appropriate tissue available for histologic evaluation; the minimum surgery required was an abdominal surgery providing tissue for histologic evaluation and establishing and documenting the primary site and stage, as well as a maximal effort at tumor debulking; if additional surgery was performed, it should have been in accordance with appropriate surgery for ovarian or peritoneal carcinoma described in the Gynecologic Oncology Group (GOG) Surgical Procedures Manual; however, the surgeon is not required to have performed all of the items contained in this section of the GOG Surgical Procedures Manual; those patients with stage III cancer in which the largest maximal diameter of any residual tumor implant at the completion of this initial surgery is no greater than 1 cm will be defined as "optimal;" all others will be defined as "suboptimal;" measurable disease on post-operative imaging studies is not required for eligibility * Patients with the following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell a…