Pembrolizumab, Carboplatin, and Paclitaxel in Treating Patients With Stage III-IV Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Signed, written informed consent * Histology showing high-grade epithelial non-mucinous ovarian, primary peritoneal, or fallopian tube cancer * No more than 4 prior cycles of chemotherapy for primary advanced (stage III or IV) epithelial ovarian, primary peritoneal, or fallopian tube cancer * No prior treatment involving irradiation, hormonal therapy, immunotherapy, investigational therapy, and/or other concurrent agents or therapies for ovarian cancer * A disposition to neoadjuvant chemotherapy with planned interval tumor reductive surgery after 4 complete cycles of treatment * Planned dose-dense chemotherapy with combination carboplatin and paclitaxel given intravenously * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Measurable disease is defined at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each "target" lesion must be \>= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \>= 10 mm when measured by spiral CT * Patients with non-measurable but evaluable solid tumors may be deemed eligible contingent upon principal investigator (PI) review * Peripheral neuropathy grade 0 or 1 by National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 * Tissue from an archival tissue sample or fresh tissue obta…