A Study to Evaluate Dostarlimab Plus Carboplatin-paclitaxel Versus Placebo Plus Carboplatin-paclitaxel in Participants With Recurrent or Primary Advanced Endometrial Cancer

Inclusion Criteria: Part 1 and Part 2: * Female participant is at least 18 years of age. * Participant has histologically or cytologically proven endometrial cancer with recurrent or advanced disease. * Participant must have primary Stage III or Stage IV disease or first recurrent endometrial cancer with a low potential for cure by radiation therapy or surgery alone or in combination and meet at least one of the following criteria; 1. Participant has primary Stage IIIA to IIIC1 disease with presence of evaluable or measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version (v).1.1 based on Investigator's assessment. Lesions that are equivocal or can be representative of post-operative change should be biopsied and confirmed for the presence of tumor; 2. Participant has primary Stage IIIC1 disease with carcinosarcoma, clear cell, serous, or mixed histology (containing greater than or equal to \[\>=\] 10 percent carcinosarcoma, clear cell, or serous histology) regardless of presence of evaluable or measurable disease on imaging; 3. Participant has primary Stage IIIC2 or Stage IV disease regardless of the presence of evaluable or measurable disease; 4. Participant has first recurrent disease and is naïve to systemic anticancer therapy; 5. Participant has received prior neo-adjuvant/adjuvant systemic anticancer therapy and had a recurrence or progression of disease (PD) \>=6 months after completing treatment (first recurrence only). * Participant has an ECOG performance status of 0 or 1. * Participant has adequate organ function. Part 2 only: * Participants must have normal blood pressure (BP) or adequately treated and controlled hypertension (systolic BP lesser than or equal to \[\<=\] 140 millimeter of mercury \[mmHg\] and diastolic BP \<=90 mmHg). * Participants must be able to take medication orally, by mouth (PO). Exclusion Criteria: Part 1 and Part 2: * Participant has received neo-adjuvant/adjuvant systemic anticancer therapy for primary Stage III or IV disease and: 1. has not had a recurrence or PD prior to first dose on the study OR 2. has had a recurrence or PD within 6 months of completing systemic anticancer therapy treatment prior to first dose on the study. * Participant has had \>1 recurrence of endometrial cancer. * Participant has received prior therapy with an anti-programmed cell death protein 1 (anti-PD-1), anti-PD-ligand 1 (anti-PD-L1), or anti-PD-ligand 2 (anti-PD-L2) agent. * Participant has received prior anticancer therapy (chemotherapy, targeted therapies, hormonal therapy, radiotherapy, or immunotherapy) within 21 days or \<5 times the half-life of the most recent therapy prior to Study Day 1, whichever is shorter. * Participant has a concomitant malignancy, or participant has a prior non-endometrial invasive malignancy who has been disease-free for \<3 years or who received any active treatment in the last 3 years for that malignancy. Non-melanoma skin cancer is allowed. * Participant has known uncontrolled central nervous system metastases, carcinomatosis meningitis, or both. * Participant has not recovered (that is \[i.e.\], to Grade \<=1 or to Baseline) from cytotoxic therapy induced AEs or has received transfusion of blood products (including platelets or red blood cells) or administration of colony-stimulating factors (including granulocyte colony-stimulating factor \[G-CSF\], granulocyte macrophage colony-stimulating factor \[GM-CSF\], or recombinant erythropoietin) within 21 days prior to the first dose of study drug. * Participant has not recovered adequately from AEs or complications from any major surgery prior to starting therapy. * Participant is currently participating and receiving study treatment or has participated in a study of an investigational agent and received study treatment or used an investigational device within 4 weeks of the first dose of treatment. * Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active infection requiring systemic therapy. * Participant has received, or is scheduled to receive, a live vaccine within 30 days before first dose of study treatment, during study treatment, and for up to 180 days after receiving the last dose of study treatment. Part 2 only: * Participant has received prior therapy with a poly (adenosine diphosphate \[ADP\]-ribose) polymerase (PARP) inhibitor. * Participant has clinically significant cardiovascular disease. * Participant has any known history or current diagnosis of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). * Participant is at increased bleeding risk due to concurrent conditions. * Participant has participated in Part 1 of this study