Inclusion Criteria:

          -  Has a histologically confirmed diagnosis of muscle-invasive bladder cancer (MIBC) with
             predominant urothelial histology

          -  Has clinically non-metastatic bladder cancer (N0M0)

          -  Has planned and is eligible to receive chemoradiotherapy (CRT) and one of the
             protocol-specified radiosensitizing chemotherapy regimens

          -  Has Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2

          -  Demonstrates adequate organ function

          -  Male participants are eligible to participate if they agree to the following during
             the intervention period and for at least 90 days after the last dose of CRT treatment:

               -  Refrain from donating sperm

               -  Be abstinent from heterosexual intercourse as their preferred and usual lifestyle
                  (abstinent on a long term and persistent basis) and agree to remain abstinent; or
                  must agree to use contraception unless confirmed to be azoospermic

          -  A female participant is eligible to participate if she is not pregnant or
             breastfeeding, and at least one of the following conditions applies:

               -  Is not a woman of childbearing potential (WOCBP)

               -  Is a WOCBP and using a contraceptive method that is highly effective (with a
                  failure rate of <1% per year), with low user dependency or be abstinent from
                  heterosexual intercourse as their preferred and usual lifestyle (abstinent on a
                  long term and persistent basis), during the intervention period and for at least
                  180 days the time needed to eliminate each study intervention after the last dose
                  of study intervention; and agrees not to donate eggs (ova, oocytes) to others or
                  freeze/store for her own use for the purpose of reproduction during this period.
                  The length of time required to continue contraception for each study intervention
                  is as follows: MK-3475 - 120 days and CRT - 180 days

        Exclusion Criteria:

          -  Has the presence of diffuse carcinoma in situ (CIS) (multiple foci of CIS) throughout
             the bladder

          -  Has the presence of urothelial carcinoma (UC) at any site outside of the urinary
             bladder in the previous 2 years except for Ta stage/T1 stage/CIS of the upper tract if
             the participant has undergone a complete nephroureterectomy

          -  Has a known additional malignancy that is progressing or has required active therapy
             within the past 3 years, except basal cell carcinoma of the skin, squamous cell
             carcinoma of the skin, superficial bladder cancer or other carcinoma in situ that has
             undergone potentially curative therapy

          -  Has the presence of bilateral hydronephrosis

          -  Has limited bladder function with frequency of small amounts of urine (< 30 mL),
             urinary incontinence, or requires self-catheterization or a permanent indwelling
             catheter

          -  Has received prior pelvic/local radiation therapy or any antineoplastic treatment for
             muscle-invasive bladder cancer (MIBC). Treatment for non-muscle invasive bladder
             cancer (NMIBC) with intravesical instillation therapy that was completed ≥28 days
             prior to randomization is allowed. Prior systemic treatment of NMIBC is not permitted.

          -  Received prior therapy with an anti-PD-1 (programmed cell death protein 1), anti-PD-L1
             (programmed death-ligand 1), or anti-PD-L2 (programmed cell death 1 ligand 2), or with
             an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g.,
             CTLA-4 [cytotoxic T-lymphocyte-associated protein 4], OX 40, or CD137 [cluster of
             differentiation 137])

          -  Has received a live vaccine within 30 days prior to the first dose of study drug

          -  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 intervention

          -  Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or the selected
             chemotherapy regimen, and/or any of their excipients

          -  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 to the first dose of study drug

          -  Has an active autoimmune disease that has required systemic treatment in the 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 human immunodeficiency virus (HIV) infection

          -  Has a known history of Hepatitis B or known active Hepatitis C virus infection

          -  Has a known history of active tuberculosis (TB; Bacillus tuberculosis)

          -  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