Study of Chemotherapy With Pembrolizumab (MK-3475) Followed by Maintenance With Olaparib (MK-7339) for the First-Line Treatment of Women With BRCA Non-mutated Advanced Epithelial Ovarian Cancer (EOC) (MK-7339-001/KEYLYNK-001/ENGOT-ov43/GOG-3036)

Has mucinous, germ cell, or borderline tumor of the ovary

Has a known or suspected deleterious mutation (germline or somatic) in either BRCA1 or BRCA2

Has a history of non-infectious pneumonitis that required treatment with steroids or currently has pneumonitis

Has either myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or has features suggestive of MDS/AML

Has a known additional malignancy that is progressing or has required active treatment in the last 3 years Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. ductal carcinoma in situ, cervical carcinoma in situ) that has undergone potentially curative therapy are not excluded.

Has ongoing Grade 3 or Grade 4 toxicity, excluding alopecia, following chemotherapy administered during the lead-in period

Has known active central nervous system metastases and/or carcinomatous meningitis. Participants with brain metastases may participate provided they were previously treated (except with chemotherapy) and are radiologically stable, clinically stable, and no steroids were used for the management of symptoms related to brain metastases within 14 days prior to randomization. Stable brain metastases should be established prior to the first dose of study medication lead-in chemotherapy

Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (dosing \>10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to randomization

Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs) Note: Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed.

Has a known history of active tuberculosis (TB; Bacillus Tuberculosis)

Has an active infection requiring systemic therapy

Has received colony-stimulating factors (eg, granulocyte colony stimulating factor \[G-CSF\], granulocyte macrophage colony-stimulating factor \[GM-CSF\] or recombinant erythropoietin) within 4 weeks prior to receiving chemotherapy during the lead-in period

Is considered to be of poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection

Has had surgery to treat borderline tumors, early stage EOC, or early stage fallopian tube cancer \<6 months prior to screening

Has a known history of human immunodeficiency virus (HIV) infection

Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Testing for hepatitis B or hepatitis C is required at screening only if mandated by local health authority. Note: Participants with a history of hepatitis B but who are HBsAg negative are eligible for the study

Is either unable to swallow orally administered medication or has a gastrointestinal (GI) disorder affecting absorption (e.g. gastrectomy, partial bowel obstruction, malabsorption)

Has uncontrolled hypertension

Has current, clinically relevant bowel obstruction (including sub-occlusive disease), abdominal fistula or GI perforation, related to underlying EOC (for participants receiving bevacizumab)

Has a history of hemorrhage, hemoptysis or active GI bleeding within 6 months prior to randomization (for participants receiving bevacizumab)

Is a WOCBP who has a positive urine pregnancy test within 72 hours before the first dose of chemotherapy in the lead-in period and within 72 hours prior to Day 1 of Cycle 1, is pregnant or breastfeeding, or is expecting to conceive children within the projected duration of the study, starting with screening through 120 days following the last dose of pembrolizumab (or pembrolizumab placebo) and bevacizumab (if administered), at least 180 days following the last dose of olaparib (or olaparib placebo), and at least 210 days following the last dose of chemotherapy

Has received prior treatment for any stage of OC, including radiation or systemic anti-cancer therapy (e.g. chemotherapy, hormonal therapy, immunotherapy, investigational therapy)

Has received prior therapy with an anti-Programmed Cell Death-1 (anti-PD-1), anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g. cytotoxic T lymphocyte antigen-4 \[CTLA-4\], OX 40, CD137)

Has received prior therapy with either olaparib or any other poly(adenosine-ribose) polymerase (PARP) inhibitor

Has intraperitoneal chemotherapy planned or has been administered as first-line therapy

Has received a live vaccine within 30 days prior to the first dose of study treatment on Day 1 of Cycle 1

Has severe hypersensitivity (≥Grade 3) to pembrolizumab, olaparib, carboplatin, paclitaxel or bevacizumab (if using) and/or any of their excipients

Is currently receiving either strong (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate (eg, ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) inhibitors of cytochrome P450 (CYP)3A4 that cannot be discontinued for the duration of the study

Is currently receiving either strong (e.g. phenobarbital, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine, and St John's Wort) or moderate (e.g. bosentan, efavirenz, modafinil) inducers of CYP3A4 that cannot be discontinued for the duration of the study

Is currently participating or has participated in a study of an investigational agent or has used an investigational device within 4 weeks (28 days) of starting chemotherapy in the Lead-in Period

Has resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions or participant has congenital long QT syndrome

Has had an allogenic tissue/solid organ transplant, has received previous allogenic bone-marrow transplant, or has received double umbilical cord transplantation

Either has had major surgery within 3 weeks of randomization or has not recovered from any effects of any major surgery

What this study is about