Study of Pembrolizumab (MK-3475) in Combination With Adjuvant Chemotherapy With or Without Radiotherapy in Participants With Newly Diagnosed Endometrial Cancer After Surgery With Curative Intent (MK-3475-B21 / KEYNOTE-B21 / ENGOT-en11 / GOG-3053)

Inclusion Criteria:

* Has a histologically confirmed new diagnosis of Endometrial Carcinoma or Carcinosarcoma (Mixed Mullerian Tumor) and:

  * Has undergone curative intent surgery that included hysterectomy and bilateral salpingo-oophorectomy; and
  * Is at high risk for recurrence following treatment with curative intent surgery, ie: Fédération Internationale de Gynécologie et d'Obstétrique (FIGO) 2009 surgical stage I/II with myometrial invasion of non-endometrioid histology; FIGO 2009 surgical stage I/II with myometrial invasion of any histology with known aberrant p53 expression or p53 mutation; or FIGO (2009) surgical stage III or IVA of any histology.
* Is disease-free with no evidence of loco-regional disease or distant metastasis post operatively and on imaging.
* Has not received any radiation or systemic therapy, including immunotherapy, hormonal therapy, or hyperthermic intraperitoneal chemotherapy (HIPEC), in any setting including the neoadjuvant setting for endometrial cancer (EC).
* Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 7 days before randomization.
* Submission of a tumor tissue sample from current diagnosis of Endometrial Carcinoma or Carcinosarcoma for prospective determination of histology and mismatch repair (MMR) status by central vendor is required for all participants.
* Has adequate organ function within 7 days of randomization.

Exclusion Criteria:

* Has recurrent endometrial carcinoma or carcinosarcoma.
* Has uterine mesenchymal tumor such as an endometrial stromal sarcoma, leiomyosarcoma, or other types of pure sarcomas. Adenosarcomas are also not allowed.
* Has FIGO (2009) Surgical Stage I/II EC of endometrioid histology without a known aberrant p53 expression or p53 mutation.
* Is known to have a deoxyribonucleic acid (DNA) polymerase epsilon catalytic subunit A (POLE) mutation.
* Has FIGO Stage IVB disease of any histology even if there is no evidence of disease after surgery.
* Has residual tumor whether measurable or non-measurable after surgery.
* Has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 3 years.

  * Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, or other in situ cancers.
* Has received prior therapy with an anti-programmed cell death receptor 1 (PD-1), anti-programmed cell death receptor ligand 1 (PD-L1), or anti-programmed cell death receptor ligand 2 (PD-L2) agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), OX-40, CD137).
* Has received a live vaccine within 30 days before the first dose of study intervention.

  * Note: killed vaccines are allowed.
* Has a known intolerance to study intervention (or any of the excipients).
* Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks before the first dose of study intervention.

  * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent.
* Has any contraindication to the use of carboplatin or paclitaxel.
* Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of study intervention.
* Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients.
* Has an active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg, 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 history of (non-infectious) pneumonitis that required steroids or has current pneumonitis.
* Has an active infection requiring systemic therapy.
* Has a known history of HIV infection.
* Has a known history of Hepatitis B or known active Hepatitis C virus infection.
* Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study.
* Has had an allogenic tissue/solid organ transplant.
* Has not recovered adequately from surgery and/or any complications from the surgery.
* Is breastfeeding.