Question: Baylor University and Duke University, are both what type of universities?
Context: Baylor University (BU) is a private Baptist university in Waco, Texas.  Chartered in 1845 by the last Congress of the Republic of Texas, it is the oldest continuously-operating university in Texas and one of the first educational institutions west of the Mississippi River in the United States.  Located on the banks of the Brazos River next to I-35, between the Dallas-Fort Worth Metroplex and Austin, the university's 1,000-acre campus is the largest Baptist university campus in the world. The Triangle Universities Nuclear Laboratory, abbreviated as TUNL (pronounced as "tunnel"), is a tripartite research consortium operated by Duke University, the University of North Carolina at Chapel Hill, and North Carolina State University.  The laboratory is located on the West Campus of Duke University in Durham, North Carolina.  Researchers are now drawn from several other universities around the United States in addition to members from the founding universities.  TUNL also participates in long term collaborations with universities and laboratories around the world.  Funding for TUNL comes primarily from the United States Department of Energy Office of Nuclear Physics. David E. Garland (born September 24, 1947) served as the interim president of Baylor University, in Waco, Texas.  His term began in June 2016 and concluded May 31, 2017.  He is credited for leading the school during its arguably two most tumultuous and difficult periods by exhibiting servant-leadership, restoring values, reconciling relationships, and creating an environment for possible future growth.  For example, during his second interim-presidency, the university reports he was able to implement all 105 recommendations related to the institution's response to sexual violence.  He expanded Baylor's parental leave and adoption assistance benefits; established student services such as the Beauchamp Addiction Recovery Center; and committed to join other universities such as Duke, Harvard, Michigan and UCLA in educating a combined 50,000 more high-achieving, lower-income students by 2025.  In appreciation for his services during two occasions as interim president, the David E. Garland Scholarship Fund was established.  The fund is dedicated to scholarships for students at Baylor's George W. Truett Theological Seminary, where Dr. Garland continues to teach. The Baylor University sexual assault scandal was the result of numerous allegations and a conviction for sexual and non-sexual assaults committed by Baylor Bears football players at Baylor University between the years 2012 and 2016.  In 2016, Baylor's football team came under fire when it was revealed university officials had failed to take action regarding the alleged rapes and other assaults.  The scandal led to the ouster of head football coach Art Briles, the demotion and eventual resignation of Baylor University President Ken Starr, the resignation of Athletic Director Ian McCaw, and the firing of two others connected with the football program.  It also led to the resignation of the Title IX Coordinator, Patty Crawford. The Golden Wave Band or GWB is a 300-member marching band associated with Baylor University.  Known at various times as the Baylor Bear Band, the Golden Wave, BUGWB (the Baylor University Golden Wave Band), and the Golden Wave Band, the GWB performs both on and off campus.  In addition to performing at regular season football games and bowls, the marching band participates in regional and state-level marching contests, such as the UIL State Marching Contest and regional marching festivals.  The music and drills performed by the band represent a corps style of marching and include both traditional and contemporary musical styles.  Members of the Golden Wave Band span all majors and fields.  Students from engineering, education, pre-law, pre-medicine, religion, University Scholars, as well as music share their musical talents with the Golden Wave. L. Gregory Jones (born 1960) is the current executive vice president and provost of Baylor University.  He formerly served as vice president and vice provost for global strategy and programs at Duke University (a position that he served for a short period).  He is also professor of theology in the Duke Divinity School.  In addition, he serves as senior strategist for Leadership Education at Duke Divinity.  From 1997-2010 he was Dean of Duke Divinity School.  He graduated with a B.A. in communications and M.P.A. from the University of Denver, an M.Div.  from Duke Divinity School and a Ph.D. in theology from Duke University.  He is the author or editor of fourteen books. Duke University is a private research university located in Durham, North Carolina.  Founded by Methodists and Quakers in the present-day town of Trinity in 1838, the school moved to Durham in 1892.  In 1924, tobacco and electric power industrialist James Buchanan Duke established The Duke Endowment, at which time the institution changed its name to honor his deceased father, Washington Duke. Duke University School of Law (also known as Duke Law School or Duke Law) is the law school and a constituent academic unit of Duke University, Durham, North Carolina, United States.  One of Duke's 10 schools and colleges, the School of Law began as the Trinity College School of Law in 1868.  In 1924, following the renaming of Trinity College to Duke University, the school was renamed the Duke University School of Law.  Notable alumni include former President of the United States Richard Nixon, esteemed television personality Charlie Rose, and United States Solicitor General Kenneth Starr. Duke University Medical Center (commonly referred to as Duke University Hospital) is a 938-acute care bed academic tertiary care facility located in Durham, North Carolina.  Since its establishment in 1930, the hospital has grown from a small regional hospital to a world-renowned academic medical center.  Duke University Hospital is the flagship teaching hospital for the Duke University Health System, a network of physicians and hospitals serving Durham County and Wake County, North Carolina, and surrounding areas, as well as one of three Level I referral centers for the Research Triangle of North Carolina (the other two are UNC Hospitals in nearby Chapel Hill and WakeMed Raleigh in Raleigh). The 1950 Baylor Bears football team represented Baylor University in the 1950 college football season.  The Bears placed second in the Southwest Conference with an overall record of 7–3.  Two players - Larry Isbell (Back) and Harold Riley (End) - were selected as All-Southwest Conference players.  The 1950 season was the inaugural season for Baylor University's new state of the art 50,000 seat Baylor Stadium.
Answer: private