[statement] + 吧
吧 at the end of a sentence turns it into a suggestion. The sentence stays as it is; 吧 takes the edge off.
Without 吧, 你坐 is an order. With it, the listener is being offered something rather than told.
吧 on a statement marks something you believe but aren't sure of, and invites the listener to confirm it. 吗 asks with no guess behind it: 你是学生吗 asks, 你是学生吧 already thinks so.
On its own, 好吧 concedes rather than agrees: it is closer to "fine, all right" than to 好.