[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 also marks a statement the speaker believes but is not sure of, and invites confirmation.
吗 asks a genuine question with no guess behind it; 吧 assumes an answer. 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.