Your carb is probably from a Chicken Power bicycle engine. The primer wasn't needed because the fuel tank is mounted above the carb and the rubber stopper type carbs are the newest style. Hopefully the little rubber thingy isn't dried out and hard because we haven't found a way to replace just the little rubber, only change the whole arm if you can find one. Member Webhead may have some if you need one, he is also the same guy who sells the diaphragms on ebay. A good remote control fuel line check valve may substitute but I haven't had the need to try that yet. That's all that little ball or rubber does, check valve the fuel so it only flows in the direction of the carb. You can test that rubber valve by connecting a clean piece of fuel line and see if you can suck air past the valve. if you can, the arm will need to be replaced unless you can get it to seal properly.
A new diaphragm will help pump enough fuel and usually needed to get these engines running.
