This study focuses on individuals who have undergone recent coronary artery bypass graft surgery (CABG), also known as bypass surgery. The purpose of the study is to compare 2 commonly used treatment strategies for the prevention of thromboembolic events (blood clots) in patients with new post-operative atrial fibrillation. Atrial fibrillation is the most common type of irregular heartbeat that occurs in some patients after they undergo CABG. It can develop when the upper chambers of the heart (atria) produce a disorganized electrical activity, which then causes the heart to beat irregularly. Patients who have this heartbeat irregularity are at a higher risk of developing blood clots in the heart. There are 2 classes of drugs for preventing blood clots: antiplatelet drugs (such as aspirin, clopidogrel or ticagrelor) and anticoagulants (blood thinners such as coumadin, apixaban, rivaroxaban, edoxaban or dabigatran). Participants will be randomly assigned to 1 of 2 groups. One group will receive an antiplatelet drug alone, and the other will receive an anticoagulant drug in addition to the antiplatelet drug. All drugs used in this study are approved by the U.S Food and Drug Administration (FDA) for patients with atrial fibrillation.