Inclusion Criteria:

          -  Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without
             small cell histology

          -  Has prostate cancer progression while on androgen deprivation therapy (or post
             bilateral orchiectomy) within 6 months prior to screening

          -  Has current evidence of metastatic disease documented by either bone lesions on bone
             scan and/or soft tissue disease by computed tomography/magnetic resonance imaging
             (CT/MRI)

          -  Has received prior treatment with one (but not more than one) NHA (eg, abiraterone
             acetate, enzalutamide, apalutamide, or darolutamide) for metastatic hormone-sensitive
             prostate cancer (mHSPC) or castration-resistant prostate cancer (CRPC) and either a)
             progressed through treatment OR b) has become intolerant of the drug

          -  Has ongoing androgen deprivation with serum testosterone <50 ng/dL (<2.0 nM)

          -  Participants receiving bone resorptive therapy (including, but not limited to,
             bisphosphonate or denosumab) must have been on stable doses prior to randomization

          -  Participants must agree to the following during the study treatment period and for at
             least 120 days after the last dose of pembrolizumab or for at least 180 days after the
             last dose of docetaxel (whichever is longer): Refrain from donating sperm PLUS Use
             contraception unless confirmed to be azoospermic (vasectomized or secondary to medical
             cause)

          -  Participants must agree to use male condom when engaging in any activity that allows
             for passage of ejaculate to another person of any sex

          -  Has provided newly obtained core or excisional biopsy (obtained within 12 months of
             screening) from soft tissue not previously irradiated (samples from tumors progressing
             in 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 past 2 years

          -  Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy

          -  Has undergone major surgery including local prostate intervention (excluding prostate
             biopsy) within 28 days prior to randomization and not recovered adequately from the
             toxicities and/or complications

          -  Has a gastrointestinal disorder affecting absorption or is unable to swallow
             tablets/capsules

          -  Has an active infection (including tuberculosis) requiring systemic therapy

          -  Has a history of (non-infectious) pneumonitis that required steroids or current
             pneumonitis

          -  Has known active human immunodeficiency virus (HIV), hepatitis B virus (HBV) or
             hepatitis C virus (HCV) infection

          -  Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis

          -  Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients

          -  Has symptomatic congestive heart failure (New York Heart Association Class III or IV
             heart disease)

          -  Has had a prior anti-cancer monoclonal antibody (mAb) prior to randomization or who
             has not recovered (i.e., Grade ≤1 or at baseline) from AEs due to mAbs

          -  Has used herbal products that may have hormonal anti-prostate cancer activity and/or
             are known to decrease PSA levels (e.g. saw palmetto) prior to randomization

          -  Has received prior treatment with radium or other therapeutic radiopharmaceuticals for
             prostate cancer

          -  Has received prior therapy with an anti-programmed cell death-1 (anti-PD-1),
             anti-programmed cell death-ligand 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-associated protein 4 [CTLA-4], OX-40, CD137)

          -  Has received prior treatment with docetaxel or another chemotherapy agent for mCRPC

          -  Has hypersensitivity to docetaxel or polysorbate 80

          -  Is currently receiving either strong or moderate inhibitors of cytochrome P450
             (CYP)3A4 that cannot be discontinued for the duration of the study

          -  Has received prior targeted small molecule therapy or abiraterone acetate,
             enzalutamide, apalutamide, or darolutamide within 4 weeks prior to the first dose of
             study treatment, or has not recovered (i.e., Grade ≤1 or at baseline) from AEs due to
             a previously administered agent

          -  Has received prior radiotherapy to within 2 weeks of start of study treatment.
             Participants must have recovered from all radiation-related toxicities, not require
             corticosteroids, and not have had radiation pneumonitis

          -  Has received a live vaccine within 30 days prior to randomization

          -  Has received treatment with 5α reductase inhibitors (eg, finasteride or dutasteride),
             estrogens, and/or cyproterone within 4 weeks prior to randomization

          -  Has received prior treatment with ketoconazole for prostate cancer

          -  Is currently participating in or has participated in a study of an investigational
             agent or has used an investigational device within 4 weeks prior to the first dose of
             study treatment

          -  Has a "superscan" bone scan

          -  Is expecting to conceive or father children within the projected duration of the
             study, starting with the screening visit through 120 days after the last dose of study
             treatment

          -  Has had an allogenic tissue/solid organ transplant