digital logic - A transistor AND gate outputs a small current when one of the inputs is HIGH. Why does this happen?

I built a simple transistor AND gate as specified by the following schematic:

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/trangate.html#c1

It works very well, however it outputs a small amount of current when input B is HIGH, enough to illuminate a standard 3mm LED. Why does this happen? How can it be prevented? Ultimately I would like this circuit to illuminate the LED only when both inputs are set to HIGH.