A Study of Atezolizumab Versus Placebo in Combination With Paclitaxel, Carboplatin, and Bevacizumab in Participants With Newly-Diagnosed Stage III or Stage IV Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria:

Participants receiving a histologic diagnosis of epithelial ovarian cancer (EOC), peritoneal primary carcinoma, or fallopian tube cancer
Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2
Life expectancy greater than (>) 12 weeks
For participants who receive therapeutic anticoagulation: stable anticoagulant regimen
Availability of a representative formalin-fixed, paraffin-embedded (FFPE) tumor specimen in paraffin blocks (preferred) or at least 20 unstained slides (for detailed tissue requirements at screening)

Exclusion Criteria:

Received a current diagnosis of borderline epithelial ovarian tumor (formerly tumors of low malignant potential)
Have recurrent invasive epithelial ovarian, fallopian tube, or primary peritoneal cancer that was treated only with surgery (example [e.g.], participants with Stage IA or Stage IB epithelial ovarian or fallopian tube cancers)
Have non-epithelial ovarian tumors (e.g., germ cell tumors, sex cord stromal tumors)
Received prior radiotherapy to any portion of the abdominal cavity or pelvis
Received prior chemotherapy for any abdominal or pelvic tumor that include neoadjuvant chemotherapy (NACT) for ovarian, primary peritoneal or fallopian tube cancer
Received any biological and/or targeted therapy (including but not limited to vaccines, antibodies, tyrosine kinase inhibitors) or hormonal therapy for management and/or treatment of epithelial ovarian or peritoneal primary cancer
Have synchronous primary endometrial cancer
Have a prior history of primary endometrial cancer, except: Stage IA cancer; superficial myometrial invasion, without lymphovascular invasion; grade less than (<) 3 or poorly differentiated subtypes, and this includes papillary serous, clear cell or other International Federation of Gynecological Oncologists (FIGO) Grade 3 lesions
With the exception of non-melanoma skin cancer and other specific malignancies as noted above, other invasive malignancies with any evidence of other cancers present within the last 5 years or previous cancer treatment that contraindicates this protocol therapy
Have a known hypersensitivity or allergy to biopharmaceutical agents produced in Chinese hamster ovary cells or any component of the atezolizumab and/or bevacizumab formulations
Undergo major surgical procedure within 28 days prior to first bevacizumab dose, or anticipation of the need for a major surgical procedure during the course of the study except participants who receive NACT and will need interval surgery. This may include but is not limited to laparotomy.
Have prior allogeneic bone marrow transplantation or solid organ transplant
Have any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results
Have any approved or investigational anti-cancer therapy, including chemotherapy or hormonal therapy, with exceptions: Hormone-replacement therapy or oral contraceptives
Are administered treatment with any other investigational agent or participation in another clinical study with anti-cancer therapeutic intent
Have core biopsy or other minor surgical procedures within 7 days prior to the first dose of bevacizumab
Have known sensitivity to any component of bevacizumab
Have known sensitivity to any component of paclitaxel
Current treatment with anti-viral therapy for hepatitis B virus (HBV)
History of leptomeningeal disease