Participant is willing to sign a screening consent and provide pre-trial tumor material for BRAF testing (both for BRAF V^600E mutation and BRAF KIAA1549 fusion assessments)* All patients who are candidates for enrollment in stratum 5 based on their tumor histology must be pre-screened* Screening may be applied to potential stratum 1 and 2 patients Diagnostic or laboratory studies performed exclusively to determine eligibility for this trial must only be done after obtaining written informed consent from all patients or their legal guardians (if the patient is < 18 years old); when appropriate, pediatric patients will be included in all discussions; this can be accomplished through one of the following mechanisms: a) the NCI, POB screening protocol, b) an Institutional Review Board (IRB)-approved institutional screening protocol or c) the study-specific protocol; documentation of the informed consent for screening will be maintained in the patients research chart; studies or procedures that were performed for clinical indications (not exclusively to determine eligibility) may be used for baseline values even if the studies were done before informed consent was obtained Hemoglobin >= 90 g/L* Blood transfusions are allowed at any time during the screening, treatment or follow-up period, according to the center recommendations SCREENING/PRE-SCREENING REGISTRATION: Patients must have Zubrod performance status 0-1 documented within 28 days prior to screening/pre-screening registration No prior treatment with TIP with the exception when given as a bridge to treatment on protocol for patients with rapidly progressive disease who cannot wait to complete the eligibility screening process; only one cycle is allowed Diagnostic or laboratory studies performed exclusively to determine eligibility for this trial must only be done after obtaining written informed consent from all patients, which can be accomplished using the NCI, POB screening protocol; studies or procedures that were performed for clinical indications (not exclusively to determine eligibility) may be used for screening or baseline values even if the studies were done before informed consent was obtained, if the patient agrees Men treated or enrolled on this protocol must agree to use 2 adequate methods of contraception starting with the screening visit, for the duration of study participation, and through 120 days after the last dose of MK-3475 administration Patients must meet all SCREENING/PRE-SCREENING and SUB-STUDY REGISTRATION COMMON ELIGIBILITY CRITERIA as specified in S1400: Phase II/III Biomarker-Driven Master Protocol for Previously Treated Squamous Cell Lung Cancer (Lung-Map) Patents must be scheduled for routine screening DBT Patient must be asymptomatic for breast disease and undergoing routine screening Patient must agree to not undergo screening ultrasound (of breast) for the duration of the 1 year study period Patients who are pregnant, nursing, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of MK-3475 (pembrolizumab) Diagnostic or laboratory studies performed exclusively to determine eligibility for this trial must only be done after obtaining written informed consent from all patients, which can be accomplished using the study specific informed consent or another consent, such as the National Cancer Institute (NCI), Pediatric Oncology Branch (POB) screening protocol; studies or procedures that were performed for clinical indications (not exclusively to determine eligibility) may be used for screening or baseline values even if the studies were done before informed consent was obtained, if the patient agrees Patients must have normal organ and marrow function independent of transfusion for at least 7 days prior to screening and independent of growth factor support for at least 14 days prior to screening Patients with known active cancers who are on therapy for those cancers at time of screening Patients must meet all SCREENING/PRE-SCREENING and SUB-STUDY REGISTRATION COMMON ELIGIBILITY CRITERIA as specified in S1400: Phase II/III Biomarker-Driven Master Protocol for Previously Treated Squamous Cell Lung Cancer (Lung-Map) Patients must be scheduled for, or have intent to schedule, a screening mammogram Patients must not have had a screening mammogram within the last 11 months prior to date of randomization ANNUAL SCREENING REGIMEN ELIGIBILITY CHECK For those women who cannot be assigned to annual or biennial screening at the time of study entry and randomization because they are postmenopausal, have no family history or known deleterious breast cancer mutation, are not on hormone therapy AND for whom a prior mammogram interpretation is not available, breast density will be determined by the radiologists recording of it at the time of interpretation of the first study screening examination, either DM or TM; for those who are randomized to TM, radiologists will assign BI-RADS density through review of the DM or synthetic 2D portion of the TM examination; such women cannot be part of the planned stratification by screening frequency and are expected to represent far less than 1% of the Tomosynthesis Mammographic Imaging Screening Trial (TMIST) population Breast density will be determined by prior mammography reports, when available, or by radiologist review of prior imaging; all other risk factors used to determine patient eligibility for annual or biennial screening will be determined by subject self-report