This is a study of pembrolizumab (MK-3475) in participants with metastatic castration-resistant prostate cancer (mCRPC). Participants will be enrolled into one of five cohorts: Cohort 1 (participants with programmed cell death ligand 1 [PD-L1]-positive, measurable disease), Cohort 2 (participants with PD-L1 negative, measurable disease), Cohort 3 (participants with bone-metastases and non-measurable disease) post-chemotherapy, Cohort 4 (participants with Response Evaluation Criteria in Solid Tumors version 1.1- [RECIST 1.1]-measureable disease) and Cohort 5 (participants with bone metastases only or bone-predominant disease) pre-chemotherapy.