Study of Olaparib (MK-7339) in Combination With Pembrolizumab (MK-3475) in the Treatment of Homologous Recombination Repair Mutation (HRRm) and/or Homologous Recombination Deficiency (HRD)-Positive Advanced Cancer (MK-7339-007/KEYLYNK-007)

Inclusion Criteria: * Has a histologically- or cytologically-confirmed advanced (metastatic and/or unresectable) solid tumor (except breast or ovarian cancers whose tumor has a germline or somatic BRCA mutation) that is not eligible for curative treatment and for which standard of care therapy has failed. Participants must have progressed on or be intolerant to standard of care therapies that are known to provide clinical benefit. There is no limit on the number of prior treatment regimens. * Has either centrally-confirmed known or suspected deleterious mutations in ≥1 of the specified 15 genes involved in HRR or centrally-confirmed HRD based on the Lynparza HRR-HRD assay. * Has measurable disease per RECIST 1.1 as assessed by the local site investigator/radiology and confirmed in real time by blinded independent central review (BICR). BICR must confirm the presence of radiologically measurable disease per RECIST 1.1 for the participant to be eligible for the study. * Has a life expectancy of ≥3 months. * Must have had CR or PR while on the last treatment with prior cisplatin or carboplatin, or if received only oxaliplatin had CR, PR, or stable disease (SD) while on the last treatment with prior oxaliplatin (either as monotherapy or in combination) for advanced (metastatic and/or unresectable) solid tumor. Participant must also not have been refractory to prior platinum-containing therapy. * Has an Eastern Cooperative Oncology Group (ECOG) performance status of either 0 or 1, as assessed within 3 days of study treatment initiation. * Male participants must agree to use contraception during the treatment period and for ≥90 days (3 months) after the last dose of olaparib and refrain from donating sperm during this period. * Female participants must not be pregnant or breastfeeding, and ≥1 of the following conditions applies: Is not a woman of childbearing potential (WOCBP) OR Is a WOCBP who agrees to use contraception during the treatment period and for ≥120 days (3 months) after the last dose of pembrolizumab and 180 days (6 months) after the last dose of olaparib, has a highly sensitive pregnancy test within 24 hours for urine or within 72 hours for serum before the first dose of study intervention, and abstains from breastfeeding during the study intervention period and for at least 120 days after the last dose of the study intervention. * Has adequate organ function Exclusion Criteria: * Has a known additional malignancy that is progressing or has required active treatment in the last 3 years. Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, ductal carcinoma in situ, or cervical carcinoma in situ that has undergone potentially curative therapy are not excluded. * Has a history of non-infectious pneumonitis/interstitial lung disease that required treatment with steroids or currently has pneumonitis/interstitial lung disease. * Has myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with features suggestive of MDS/AML. * Has known central nervous system (CNS) metastases and/or carcinomatous meningitis. * Has an active infection requiring systemic therapy. * Has active tuberculosis (Bacillus tuberculosis \[TB\]). * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (dosing \>10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment. * Has an active autoimmune disease that has required systemic treatment in the past 2 years. * Has received colony-stimulating factors (e.g. granulocyte colony-stimulating factor \[G-CSF\], granulocyte-macrophage colony-stimulating factor \[GM-CSF\] or recombinant erythropoietin) within 28 days prior to the first dose of study treatment. * Has a known history of human immunodeficiency virus (HIV) infection. * Has known active hepatitis B or hepatitis C. * Is unable to swallow orally administered medication or has a gastrointestinal (GI) disorder affecting absorption (e.g. gastrectomy, partial bowel obstruction, malabsorption). * Has received prior therapy with an anti-programmed death-1 (anti-PD-1), anti-programmed death-ligand 1 (anti-PD-L1), or anti-programmed death-ligand 2 (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 \[Tumor necrosis factor receptor superfamily, member 4 (TNFRSF4)\], CD137 \[tumor necrosis factor receptor superfamily member 9 (TNFRSF9)\]). * Has received prior therapy with olaparib or with any other polyadenosine 5' diphosphoribose (poly\[ADP ribose\]) polymerization (PARP) inhibitor. * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to administration of study treatment. * Must have recovered from all adverse events (AEs) due to previous therapies, excluding alopecia, to ≤Grade 1 or Baseline. * Has a known hypersensitivity to the study treatments and/or any of their excipients. * Is currently receiving either strong inhibitors of cytochrome P450 (CYP)3A4 (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate inhibitors of CYP3A4 (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 2 weeks. * Is currently receiving either strong inducers of CYP3A4 (phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate inducers of CYP3A4 (e.g. bosentan, efavirenz, modafinil) that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 5 weeks for phenobarbital and 3 weeks for other agents. * Has received previous allogenic bone-marrow transplant or double umbilical cord transplantation (dUCBT). * Has received a whole blood transfusion in the last 120 days prior to entry to the study. * Has received prior radiotherapy within 2 weeks of start of study treatment. * Is currently enrolled in and receiving study therapy, was enrolled in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks (28 days) of the first dose of study treatment. * The presence of uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g. unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, corrected QT interval by Fredericia \[QTcF\] prolongation \>500 msec, electrolyte disturbances), or participant has congenital long QT syndrome. * Has either had major surgery within 2 weeks of starting study treatment or has not recovered from any effects of any major surgery. * Has received a live vaccine within 30 days prior to the first dose of study treatment. * Has had an allogenic tissue/solid tumor organ transplant.