A Study of Pembrolizumab (MK-3475) in Relapsed or Refractory Classical Hodgkin's Lymphoma (rrcHL) or Relapsed or Refractory Primary Mediastinal Large B-cell Lymphoma (rrPMBCL) (MK-3475-B68)

Inclusion Criteria:

* Have a histologically confirmed diagnosis of cHL or PMBCL, according to the World Health Organization (WHO) classification \[Swerdlow, S. H., et al 2008\].
* Has radiographically measurable cHL or PMBCL disease as per Lugano classification with at least 1 nodal lesion (which has not been previously radiated) that is \>15 mm in long axis, regardless of the length of the short axis, and/or extranodal lesion of \>10 mm in long and short axis.

PMBCL-Specific Disease Characteristics:

* Have relapsed or refractory PMBCL and:
* Have relapsed after auto-stem cell transplant (SCT) or have failed to achieve a CR or PR within 60 days of auto-SCT. Participants may have received intervening therapy after auto-SCT for relapsed or refractory disease, in which case they must have relapsed after or be refractory to their last treatment.

OR

\- For participants who are ineligible for auto-SCT, have received at least ≥2 lines of prior therapy and have failed to respond to or relapsed after their last line of treatment. At least 1 of the prior lines of therapy must contain a rituximab-based regimen.

Note: Participants should not need urgent cytoreductive therapy.

* Relapsed Disease: disease progression after achieving an overall response of PR or CR in response to the most recent therapy
* Refractory Disease: failure to achieve CR or PR to the most recent therapy.

cHL-Specific Disease Characteristics:

* Have relapsed or refractory cHL and:
* Have relapsed during their last cHL regimen after receiving at least 2 cycles of therapy or within 12 months after completing the last regimen for cHL.

OR

* Have received at least ≥1 line of prior multiagent therapy with/without brentuximab vedotin (excluding radiation) or auto-SCT for cHL and have failed to respond to or relapsed after their last line of treatment.

  * Relapsed Disease: disease progression after achieving an overall response of PR or CR to the most recent therapy.
  * Refractory Disease: failure to achieve CR or PR to the most recent therapy.
* 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 child bearing potential (WOCBP). OR
* Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis), for at least 120 days after the last dose of study intervention.
* Submit an evaluable core lymph node biopsy for biomarker analysis from an archival (\>60 days) or newly obtained (within 30 days) core or incisional biopsy at Screening which was not previously irradiated. Note: If no archival tissue is available, 2 new fresh core needle samples are required.
* Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
* Life expectancy \>3 months.
* Adequate organ function.

Exclusion Criteria:

* Has undergone solid organ transplant at any time, or prior allogeneic hematopoietic SCT within the last 5 years
* Has clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\<6 months prior to enrollment), myocardial infarction (\<6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification Class ≥II), or serious cardiac arrhythmia requiring medication
* Has pericardial effusion or clinically significant pleural effusion
* Has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, or other in situ cancers
* Is receiving systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) \<3 days prior to the first dose of study intervention. Note: Participants who receive daily steroid replacement therapy are an exception
* Has received prior monoclonal antibody within 4 weeks prior to first dose of study intervention or has not recovered (i.e., ≤Grade 1 or at baseline) from adverse event (AEs) due to agents administered more than 4 weeks earlier
* Has received prior therapy with an anti-programmed cell death 1 protein (PD-1), anti-programmed cell death ligand 1 (PD-L1), or anti-programmed cell death ligand 2 (PD-L2) agent or with an agent directed to another stimulatory or coinhibitory T-cell receptor (e.g., CTLA-4, OX-40, CD137)
* Has received prior chimeric antigen receptor T-cell (CAR-T) therapy
* Has received prior systemic anticancer therapy, or radiotherapy, including investigational agents within 4 weeks prior to the first dose of study intervention. Note: If the participant had a major operation, the participant must have recovered adequately from the procedure and/or any complications from the operation before starting study intervention
* Has received prior radiotherapy within 2 weeks of start of study intervention or have had a history of radiation pneumonitis. Participants must have recovered from all radiation-related toxicities, and not require corticosteroids
* Has received a live or live-attenuated vaccine within 30 days before 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 before the first dose of study intervention
* 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 medication
* Has known active central nervous system (CNS) lymphoma involvement or active CNS involvement by lymphoma
* Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients
* Has an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., 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 (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease
* Has an active infection requiring systemic therapy
* Has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority
* Has a known history of Hepatitis B (defined as hepatitis B surface antigen (HBsAg) reactive) or known active Hepatitis C virus infection