When a bulb goes out in a series circuit do the rest go out too?

In simple terms yes. The circuit is made through the elements of each lamp. So if one blows then it will take the lot out. Just like Christmas tree lights. Now because of this, most xmas tree lighs are wired in parallel. This means that the voltage is constant throughout the circuit unlike a series circuit where the current is constant.

It is possible however unlikely for a lamp to blow but for the element to remain "connected" so a circuit still exists. In the case the other lamp will remain on, though this means that whatever the suppy voltage, will be distributed across this one lamp now instead of the two so it may be too much for it.

Hope this helps

CBurton

England