The purpose of this study is to assess the efficacy and safety of treatment with carboplatin/paclitaxel\* PLUS pembrolizumab (MK-3475) and maintenance olaparib (MK-7339) in women with epithelial ovarian cancer (EOC), fallopian tube cancer, or primary peritoneal cancer. The primary study hypotheses are that the combination of pembrolizumab plus carboplatin/paclitaxel\* followed by continued pembrolizumab and maintenance olaparib is superior to carboplatin/paclitaxel alone with respect to Progression Free Survival (PFS) per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) in participants with programmed death-ligand 1 (PD-L1) positive tumors (Combined Positive Score \[CPS\]≥10) and in all participants, and that the combination of pembrolizumab plus carboplatin/paclitaxel followed by continued pembrolizumab is superior to carboplatin/paclitaxel alone with respect to PFS per RECIST 1.1 in participants with PD-L1 positive tumors (CPS≥10) and in all participants.