A ripe banana has no green tips; as a banana ripens it becomes sweeter.Apple bananas are firmer than Williams bananas; they may cost a little more, but they last longer, remaining firm and sweet.Never ripen bananas in the refrigerator; the cold will stop the development of their sugars.Bananas are a good source of potassium, are high in vitamin B-6 and low in sodium and are good source of fiber.