Study of Pembrolizumab (MK-3475) Plus Olaparib Versus Abiraterone Acetate or Enzalutamide in Metastatic Castration-resistant Prostate Cancer (mCRPC) (MK-7339-010/KEYLYNK-010)

Inclusion Criteria: * Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology * Has prostate cancer progression while receiving androgen deprivation therapy (or post bilateral orchiectomy) within 6 months before screening * Has current evidence of metastatic disease documented by bone lesions on bone scan and/or soft tissue disease shown by computed tomography/magnetic resonance imaging (CT/MRI) * Has received prior treatment with abiraterone acetate OR enzalutamide, but not both * Have disease that progressed during or after treatment with abiraterone acetate for either metastatic hormone-sensitive prostate cancer (mHSPC) or mCRP or enzalutamide for mCRPC for at least 8 weeks (at least 14 weeks for participants with bone progression) * Participants that received abiraterone acetate for mHSPC may not have received abiraterone acetate or enzalutamide for mCRPC * Have received docetaxel chemotherapy regimen for metastatic castration-resistant prostate cancer (mCRPC) and have had progressive disease during or after treatment with docetaxel * Has ongoing androgen deprivation with serum testosterone \<50 ng/dL (\<2.0 nM) * If receiving bone resorptive therapy, including but not limited to bisphosphonates or denosumab, must have been receiving stable doses before randomization * Must agree to refrain from donating sperm during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention PLUS be abstinent from heterosexual intercourse OR must agree to use contraception unless confirmed to be azoospermic * Contraception use by men should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions is more stringent than the requirement above, the local label requirements are to be followed. * Has provided tumor tissue from a fresh core or excisional biopsy (obtained within 12 months of screening) from soft tissue not previously irradiated. Samples from tumors progressing at a prior site of radiation are allowed. Participants with bone-only or bone-predominant disease may provide a bone biopsy sample * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 assessed within 7 days of randomization Exclusion Criteria: * Has a known additional malignancy that is progressing or has required active treatment in the last 3 years * Has an active autoimmune disease that has required systemic treatment in the past 2 years * Has a history of (noninfectious) pneumonitis requiring steroids, or has current pneumonitis * Has known active human immunodeficiency virus (HIV), hepatitis B virus (e.g., hepatitis B surface antigen reactive) or hepatitis C virus (HCV) infection (e.g., HCV RNA \[qualitative\] is detected) * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has a history of seizure or any condition that may predispose to seizure * Has a history of loss of consciousness within 12 months of screening * Has myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or has features suggestive of MDS/AML * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy * Has (≥Grade 3) hypersensitivity to pembrolizumab and/or any of its excipients * Has known hypersensitivity to the components or excipients in olaparib, abiraterone acetate, prednisone or prednisolone, or enzalutamide * Has symptomatic congestive heart failure (New York Heart Association Class III or IV heart disease) * Has received an anticancer monoclonal antibody (mAb) before randomization * Has received prior treatment with olaparib or any other PARP inhibitor * Has received prior treatment with apalutamide or darolutamide * Has received prior treatment with enzalutamide or apalutamide for metastatic hormone-sensitive prostate cancer * Has used herbal products that may have hormonal anti-prostate cancer activity and/or are known to decrease PSA (e.g., saw palmetto) before the date of randomization * Has received prior treatment with radium or other therapeutic radiopharmaceuticals for prostate cancer * Has received prior treatment with an 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., CTLA-4, OX-40, or CD137) * Is currently receiving either strong or moderate inhibitors of cytochrome P450 \[CYP\] (CYP3A4) that cannot be discontinued for the duration of the study * Has received a previous allogenic bone marrow transplant or double umbilical cord transplantation (dUCBT) or a solid organ transplant * Has received a live vaccine within 30 days prior to the date of randomization * 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 date of randomization * Has a bone "superscan" * Is expecting to father children within the projected duration of the study, starting with the screening visit through 90 days after the last dose of study intervention